290203
36 unit squares are joined to form a rectangle with the least perimeter. Perimeter of the rectangle is:
1 12 units
2 26 units
3 24 units
4 36 units
Explanation:
26 units Area of rectangle is 36 units we have, 36 = 6 × 6 = 2 × 3 × 3 × 2 = 4 × 9 the sides of a rectangle are 4cm and 9cm Perimeter = 2(l + b) = 2(4 + 9) = 13 × 2 = 26 units
09. MENSURATION
290204
Find perimeter of a square if its diagonal is \({16}\sqrt{2}\text{cm}:\)
290205
If the perimeter of a rectangle is p and its diagonal is d, the difference between the length and width of the rectangle is:
1 \(\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}\)
2 \(\frac{\sqrt{8\text{d}^{2}+\text{p}^{2}}}{2}\)
3 \(\frac{\sqrt{6\text{d}^{2}-\text{p}^{2}}}{2}\)
4 \(\frac{\sqrt{6\text{d}^{2}+\text{p}^{2}}}{2}\)
5 \(\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{4}\)
Explanation:
\(\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}\) Perimeter of the rectangle = P2(l + b) = P ? \(\)\(1+\text{b}=\frac{\text{P}}{2}\rightarrow\) (1)diagonal of the rectangle = \(\text{d}\sqrt{1^2+\text{b}^2}=\text{d}\) \(\Rightarrow{1}^{2}+\text{b}^{2}=\text{d}^{2}\) (1)\(^{1}\)? d\(^{1}\)+ 2lb = \(\frac{\text{p}^{2}}{4}\) ? 2lb \(=\frac{\text{p}^2 - 4\text{d}^2}{4}\) l\(^{1}\) + b\(^{1}\)- 2lb = d\(^{1}\)\(^{1}\) \(\Rightarrow(1-\text{b})^{2}=\)\(^{1}\)\(^{1}\) \(\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}\) \(\therefore\) Difference between length and breadth \( = \frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}\)
09. MENSURATION
290206
If the ratio of areas of two squares is 225 : 256, then the ratio of their perimeters is:
1 225 : 256
2 256 : 225
3 15 : 16
4 16 : 15
Explanation:
15 : 16 Let the two squares be ABCD and PQRS. Further, let the lengths of each side of ABCD and PQRS be x and y, respectively. Therefore, \(\frac{\text{Area of square ABCD}}{\text{Area of square PQRS}}=\frac{\text{x}^{2}}{\text{y}^{2}}\) \(=\frac{225}{256}\) Taking square roots on both sides, we get: \(\frac{\text{x}}{\text{y}}=\frac{15}{16}\) Now, the ratio of their perimeters: \(\frac{\text{Perimeter of square ABCD}}{\text{Perimeter of square PQRS}}\) \(\frac{4\times\text{side of square ABCD}}{4\times\text{side of square PQRS}}=\frac{4\text{x}}{4\text{y}}\) \(\frac{\text{Perimeter of square ABCD}}{\text{Perimeter of square PQRS}}=\text{x}:\text{y}\) \(\frac{\text{Perimeter of square ABCD}}{\text{Perimeter of square PQRS}}=\frac{15}{16}\) Thus, the ratio of their perimeters = 15 : 16
09. MENSURATION
290207
Perimeter of a square is the sum of the lengths of all the _____ sides.
1 3
2 2
3 5
4 4
Explanation:
4 Perimeter is the sum of length of the boundaries.In a square, the sides act as the boundaries. Since a square has 44 sides, so perimeter of a square is the sum of the lengths of all the 44 sides.
290203
36 unit squares are joined to form a rectangle with the least perimeter. Perimeter of the rectangle is:
1 12 units
2 26 units
3 24 units
4 36 units
Explanation:
26 units Area of rectangle is 36 units we have, 36 = 6 × 6 = 2 × 3 × 3 × 2 = 4 × 9 the sides of a rectangle are 4cm and 9cm Perimeter = 2(l + b) = 2(4 + 9) = 13 × 2 = 26 units
09. MENSURATION
290204
Find perimeter of a square if its diagonal is \({16}\sqrt{2}\text{cm}:\)
290205
If the perimeter of a rectangle is p and its diagonal is d, the difference between the length and width of the rectangle is:
1 \(\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}\)
2 \(\frac{\sqrt{8\text{d}^{2}+\text{p}^{2}}}{2}\)
3 \(\frac{\sqrt{6\text{d}^{2}-\text{p}^{2}}}{2}\)
4 \(\frac{\sqrt{6\text{d}^{2}+\text{p}^{2}}}{2}\)
5 \(\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{4}\)
Explanation:
\(\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}\) Perimeter of the rectangle = P2(l + b) = P ? \(\)\(1+\text{b}=\frac{\text{P}}{2}\rightarrow\) (1)diagonal of the rectangle = \(\text{d}\sqrt{1^2+\text{b}^2}=\text{d}\) \(\Rightarrow{1}^{2}+\text{b}^{2}=\text{d}^{2}\) (1)\(^{1}\)? d\(^{1}\)+ 2lb = \(\frac{\text{p}^{2}}{4}\) ? 2lb \(=\frac{\text{p}^2 - 4\text{d}^2}{4}\) l\(^{1}\) + b\(^{1}\)- 2lb = d\(^{1}\)\(^{1}\) \(\Rightarrow(1-\text{b})^{2}=\)\(^{1}\)\(^{1}\) \(\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}\) \(\therefore\) Difference between length and breadth \( = \frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}\)
09. MENSURATION
290206
If the ratio of areas of two squares is 225 : 256, then the ratio of their perimeters is:
1 225 : 256
2 256 : 225
3 15 : 16
4 16 : 15
Explanation:
15 : 16 Let the two squares be ABCD and PQRS. Further, let the lengths of each side of ABCD and PQRS be x and y, respectively. Therefore, \(\frac{\text{Area of square ABCD}}{\text{Area of square PQRS}}=\frac{\text{x}^{2}}{\text{y}^{2}}\) \(=\frac{225}{256}\) Taking square roots on both sides, we get: \(\frac{\text{x}}{\text{y}}=\frac{15}{16}\) Now, the ratio of their perimeters: \(\frac{\text{Perimeter of square ABCD}}{\text{Perimeter of square PQRS}}\) \(\frac{4\times\text{side of square ABCD}}{4\times\text{side of square PQRS}}=\frac{4\text{x}}{4\text{y}}\) \(\frac{\text{Perimeter of square ABCD}}{\text{Perimeter of square PQRS}}=\text{x}:\text{y}\) \(\frac{\text{Perimeter of square ABCD}}{\text{Perimeter of square PQRS}}=\frac{15}{16}\) Thus, the ratio of their perimeters = 15 : 16
09. MENSURATION
290207
Perimeter of a square is the sum of the lengths of all the _____ sides.
1 3
2 2
3 5
4 4
Explanation:
4 Perimeter is the sum of length of the boundaries.In a square, the sides act as the boundaries. Since a square has 44 sides, so perimeter of a square is the sum of the lengths of all the 44 sides.
290203
36 unit squares are joined to form a rectangle with the least perimeter. Perimeter of the rectangle is:
1 12 units
2 26 units
3 24 units
4 36 units
Explanation:
26 units Area of rectangle is 36 units we have, 36 = 6 × 6 = 2 × 3 × 3 × 2 = 4 × 9 the sides of a rectangle are 4cm and 9cm Perimeter = 2(l + b) = 2(4 + 9) = 13 × 2 = 26 units
09. MENSURATION
290204
Find perimeter of a square if its diagonal is \({16}\sqrt{2}\text{cm}:\)
290205
If the perimeter of a rectangle is p and its diagonal is d, the difference between the length and width of the rectangle is:
1 \(\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}\)
2 \(\frac{\sqrt{8\text{d}^{2}+\text{p}^{2}}}{2}\)
3 \(\frac{\sqrt{6\text{d}^{2}-\text{p}^{2}}}{2}\)
4 \(\frac{\sqrt{6\text{d}^{2}+\text{p}^{2}}}{2}\)
5 \(\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{4}\)
Explanation:
\(\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}\) Perimeter of the rectangle = P2(l + b) = P ? \(\)\(1+\text{b}=\frac{\text{P}}{2}\rightarrow\) (1)diagonal of the rectangle = \(\text{d}\sqrt{1^2+\text{b}^2}=\text{d}\) \(\Rightarrow{1}^{2}+\text{b}^{2}=\text{d}^{2}\) (1)\(^{1}\)? d\(^{1}\)+ 2lb = \(\frac{\text{p}^{2}}{4}\) ? 2lb \(=\frac{\text{p}^2 - 4\text{d}^2}{4}\) l\(^{1}\) + b\(^{1}\)- 2lb = d\(^{1}\)\(^{1}\) \(\Rightarrow(1-\text{b})^{2}=\)\(^{1}\)\(^{1}\) \(\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}\) \(\therefore\) Difference between length and breadth \( = \frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}\)
09. MENSURATION
290206
If the ratio of areas of two squares is 225 : 256, then the ratio of their perimeters is:
1 225 : 256
2 256 : 225
3 15 : 16
4 16 : 15
Explanation:
15 : 16 Let the two squares be ABCD and PQRS. Further, let the lengths of each side of ABCD and PQRS be x and y, respectively. Therefore, \(\frac{\text{Area of square ABCD}}{\text{Area of square PQRS}}=\frac{\text{x}^{2}}{\text{y}^{2}}\) \(=\frac{225}{256}\) Taking square roots on both sides, we get: \(\frac{\text{x}}{\text{y}}=\frac{15}{16}\) Now, the ratio of their perimeters: \(\frac{\text{Perimeter of square ABCD}}{\text{Perimeter of square PQRS}}\) \(\frac{4\times\text{side of square ABCD}}{4\times\text{side of square PQRS}}=\frac{4\text{x}}{4\text{y}}\) \(\frac{\text{Perimeter of square ABCD}}{\text{Perimeter of square PQRS}}=\text{x}:\text{y}\) \(\frac{\text{Perimeter of square ABCD}}{\text{Perimeter of square PQRS}}=\frac{15}{16}\) Thus, the ratio of their perimeters = 15 : 16
09. MENSURATION
290207
Perimeter of a square is the sum of the lengths of all the _____ sides.
1 3
2 2
3 5
4 4
Explanation:
4 Perimeter is the sum of length of the boundaries.In a square, the sides act as the boundaries. Since a square has 44 sides, so perimeter of a square is the sum of the lengths of all the 44 sides.
290203
36 unit squares are joined to form a rectangle with the least perimeter. Perimeter of the rectangle is:
1 12 units
2 26 units
3 24 units
4 36 units
Explanation:
26 units Area of rectangle is 36 units we have, 36 = 6 × 6 = 2 × 3 × 3 × 2 = 4 × 9 the sides of a rectangle are 4cm and 9cm Perimeter = 2(l + b) = 2(4 + 9) = 13 × 2 = 26 units
09. MENSURATION
290204
Find perimeter of a square if its diagonal is \({16}\sqrt{2}\text{cm}:\)
290205
If the perimeter of a rectangle is p and its diagonal is d, the difference between the length and width of the rectangle is:
1 \(\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}\)
2 \(\frac{\sqrt{8\text{d}^{2}+\text{p}^{2}}}{2}\)
3 \(\frac{\sqrt{6\text{d}^{2}-\text{p}^{2}}}{2}\)
4 \(\frac{\sqrt{6\text{d}^{2}+\text{p}^{2}}}{2}\)
5 \(\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{4}\)
Explanation:
\(\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}\) Perimeter of the rectangle = P2(l + b) = P ? \(\)\(1+\text{b}=\frac{\text{P}}{2}\rightarrow\) (1)diagonal of the rectangle = \(\text{d}\sqrt{1^2+\text{b}^2}=\text{d}\) \(\Rightarrow{1}^{2}+\text{b}^{2}=\text{d}^{2}\) (1)\(^{1}\)? d\(^{1}\)+ 2lb = \(\frac{\text{p}^{2}}{4}\) ? 2lb \(=\frac{\text{p}^2 - 4\text{d}^2}{4}\) l\(^{1}\) + b\(^{1}\)- 2lb = d\(^{1}\)\(^{1}\) \(\Rightarrow(1-\text{b})^{2}=\)\(^{1}\)\(^{1}\) \(\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}\) \(\therefore\) Difference between length and breadth \( = \frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}\)
09. MENSURATION
290206
If the ratio of areas of two squares is 225 : 256, then the ratio of their perimeters is:
1 225 : 256
2 256 : 225
3 15 : 16
4 16 : 15
Explanation:
15 : 16 Let the two squares be ABCD and PQRS. Further, let the lengths of each side of ABCD and PQRS be x and y, respectively. Therefore, \(\frac{\text{Area of square ABCD}}{\text{Area of square PQRS}}=\frac{\text{x}^{2}}{\text{y}^{2}}\) \(=\frac{225}{256}\) Taking square roots on both sides, we get: \(\frac{\text{x}}{\text{y}}=\frac{15}{16}\) Now, the ratio of their perimeters: \(\frac{\text{Perimeter of square ABCD}}{\text{Perimeter of square PQRS}}\) \(\frac{4\times\text{side of square ABCD}}{4\times\text{side of square PQRS}}=\frac{4\text{x}}{4\text{y}}\) \(\frac{\text{Perimeter of square ABCD}}{\text{Perimeter of square PQRS}}=\text{x}:\text{y}\) \(\frac{\text{Perimeter of square ABCD}}{\text{Perimeter of square PQRS}}=\frac{15}{16}\) Thus, the ratio of their perimeters = 15 : 16
09. MENSURATION
290207
Perimeter of a square is the sum of the lengths of all the _____ sides.
1 3
2 2
3 5
4 4
Explanation:
4 Perimeter is the sum of length of the boundaries.In a square, the sides act as the boundaries. Since a square has 44 sides, so perimeter of a square is the sum of the lengths of all the 44 sides.
290203
36 unit squares are joined to form a rectangle with the least perimeter. Perimeter of the rectangle is:
1 12 units
2 26 units
3 24 units
4 36 units
Explanation:
26 units Area of rectangle is 36 units we have, 36 = 6 × 6 = 2 × 3 × 3 × 2 = 4 × 9 the sides of a rectangle are 4cm and 9cm Perimeter = 2(l + b) = 2(4 + 9) = 13 × 2 = 26 units
09. MENSURATION
290204
Find perimeter of a square if its diagonal is \({16}\sqrt{2}\text{cm}:\)
290205
If the perimeter of a rectangle is p and its diagonal is d, the difference between the length and width of the rectangle is:
1 \(\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}\)
2 \(\frac{\sqrt{8\text{d}^{2}+\text{p}^{2}}}{2}\)
3 \(\frac{\sqrt{6\text{d}^{2}-\text{p}^{2}}}{2}\)
4 \(\frac{\sqrt{6\text{d}^{2}+\text{p}^{2}}}{2}\)
5 \(\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{4}\)
Explanation:
\(\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}\) Perimeter of the rectangle = P2(l + b) = P ? \(\)\(1+\text{b}=\frac{\text{P}}{2}\rightarrow\) (1)diagonal of the rectangle = \(\text{d}\sqrt{1^2+\text{b}^2}=\text{d}\) \(\Rightarrow{1}^{2}+\text{b}^{2}=\text{d}^{2}\) (1)\(^{1}\)? d\(^{1}\)+ 2lb = \(\frac{\text{p}^{2}}{4}\) ? 2lb \(=\frac{\text{p}^2 - 4\text{d}^2}{4}\) l\(^{1}\) + b\(^{1}\)- 2lb = d\(^{1}\)\(^{1}\) \(\Rightarrow(1-\text{b})^{2}=\)\(^{1}\)\(^{1}\) \(\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}\) \(\therefore\) Difference between length and breadth \( = \frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}\)
09. MENSURATION
290206
If the ratio of areas of two squares is 225 : 256, then the ratio of their perimeters is:
1 225 : 256
2 256 : 225
3 15 : 16
4 16 : 15
Explanation:
15 : 16 Let the two squares be ABCD and PQRS. Further, let the lengths of each side of ABCD and PQRS be x and y, respectively. Therefore, \(\frac{\text{Area of square ABCD}}{\text{Area of square PQRS}}=\frac{\text{x}^{2}}{\text{y}^{2}}\) \(=\frac{225}{256}\) Taking square roots on both sides, we get: \(\frac{\text{x}}{\text{y}}=\frac{15}{16}\) Now, the ratio of their perimeters: \(\frac{\text{Perimeter of square ABCD}}{\text{Perimeter of square PQRS}}\) \(\frac{4\times\text{side of square ABCD}}{4\times\text{side of square PQRS}}=\frac{4\text{x}}{4\text{y}}\) \(\frac{\text{Perimeter of square ABCD}}{\text{Perimeter of square PQRS}}=\text{x}:\text{y}\) \(\frac{\text{Perimeter of square ABCD}}{\text{Perimeter of square PQRS}}=\frac{15}{16}\) Thus, the ratio of their perimeters = 15 : 16
09. MENSURATION
290207
Perimeter of a square is the sum of the lengths of all the _____ sides.
1 3
2 2
3 5
4 4
Explanation:
4 Perimeter is the sum of length of the boundaries.In a square, the sides act as the boundaries. Since a square has 44 sides, so perimeter of a square is the sum of the lengths of all the 44 sides.
