290113
The length of a rectangular verandah is 3m more than its breadth. the numerical value of its area is equal to the numerical value of its perimeter. Find the dimensions of the verandah:
1 x = 6; length = 5m and breadth = 3m
2 x = 3; length = 6m and breadth = 3m
3 x = 4; length = 4m and breadth = 2m
4 x = 5; length = 7m and breadth = 2m
Explanation:
x = 3; length = 6m and breadth = 3m Let the breadth of rectangular verandah = x therefore, length = x + 3 [According to given statement] area of the verandah = Perimeter of verandah l × b = 2(l + b) (3 + x) × x = 2(3 + x + x) 3x + x\(^{1}\) = 2(3 + 2x) x\(^{1}\) + 3x - 6 - 4x = 0 x\(^{1}\)- x - 6 = 0 x\(^{1}\)- 3x + 2x - 6 = 0 x(x - 3) + 2(x - 3) = 0 (x - 3) (x + 2) = 0 x = 3, x = - 2 Now, x = - 2 as dimension of the verandah cannot be in negative, \(\therefore\) x = 3 Length of rectangle = x + 3 = 3 + 3 = 6m Breadth of rectangle = x = 3m
09. MENSURATION
290114
The ______ of any polygon is the sum of the lengths of all the sides.
1 Volume
2 Area
3 Circumference
4 Perimete
Explanation:
Perimete The perimeter of any polygon is the sum of the lengths of all the sides. Example: In a square whose side is given as 2m, therefore, square has 4sides. Perimeter = 2 + 2 + 2 + 2 = 8m
09. MENSURATION
290115
A square shaped park ABCD of side 100m has two equal rectangular flower beds each of size 10m × 5m Length of the boundary of the remaining park is:
1 360m
2 400m
3 340m
4 460m
Explanation:
400m In order to find the length of the boundary of the remaining park, we add two flower beds each of length 10m and breadth 5m, then remaining park is shown below: Now, length of the boundary of the remaining park = Perimeter of remaining park = (90 + 5 + 10 + 95 + 90 + 5 + 10 + 95)m = 400m
09. MENSURATION
290116
If perimeter of a square is tripled, then area will be ........ of original area:
1 4 times
2 \(\frac{1}{4}\) times
3 9 times
4 \(\frac{1}{9}\) times
Explanation:
9 times S = 4SP\(_{\1}\) = 4×S' = 4S' P\(_{\1}\) = 3P thus, 4S' = 12SS = 3S A = S\(^{1}\)A = (S)\(^{1}\)A' = (3S)\(^{1}\)A' ?A' = 9A
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09. MENSURATION
290113
The length of a rectangular verandah is 3m more than its breadth. the numerical value of its area is equal to the numerical value of its perimeter. Find the dimensions of the verandah:
1 x = 6; length = 5m and breadth = 3m
2 x = 3; length = 6m and breadth = 3m
3 x = 4; length = 4m and breadth = 2m
4 x = 5; length = 7m and breadth = 2m
Explanation:
x = 3; length = 6m and breadth = 3m Let the breadth of rectangular verandah = x therefore, length = x + 3 [According to given statement] area of the verandah = Perimeter of verandah l × b = 2(l + b) (3 + x) × x = 2(3 + x + x) 3x + x\(^{1}\) = 2(3 + 2x) x\(^{1}\) + 3x - 6 - 4x = 0 x\(^{1}\)- x - 6 = 0 x\(^{1}\)- 3x + 2x - 6 = 0 x(x - 3) + 2(x - 3) = 0 (x - 3) (x + 2) = 0 x = 3, x = - 2 Now, x = - 2 as dimension of the verandah cannot be in negative, \(\therefore\) x = 3 Length of rectangle = x + 3 = 3 + 3 = 6m Breadth of rectangle = x = 3m
09. MENSURATION
290114
The ______ of any polygon is the sum of the lengths of all the sides.
1 Volume
2 Area
3 Circumference
4 Perimete
Explanation:
Perimete The perimeter of any polygon is the sum of the lengths of all the sides. Example: In a square whose side is given as 2m, therefore, square has 4sides. Perimeter = 2 + 2 + 2 + 2 = 8m
09. MENSURATION
290115
A square shaped park ABCD of side 100m has two equal rectangular flower beds each of size 10m × 5m Length of the boundary of the remaining park is:
1 360m
2 400m
3 340m
4 460m
Explanation:
400m In order to find the length of the boundary of the remaining park, we add two flower beds each of length 10m and breadth 5m, then remaining park is shown below: Now, length of the boundary of the remaining park = Perimeter of remaining park = (90 + 5 + 10 + 95 + 90 + 5 + 10 + 95)m = 400m
09. MENSURATION
290116
If perimeter of a square is tripled, then area will be ........ of original area:
1 4 times
2 \(\frac{1}{4}\) times
3 9 times
4 \(\frac{1}{9}\) times
Explanation:
9 times S = 4SP\(_{\1}\) = 4×S' = 4S' P\(_{\1}\) = 3P thus, 4S' = 12SS = 3S A = S\(^{1}\)A = (S)\(^{1}\)A' = (3S)\(^{1}\)A' ?A' = 9A
290113
The length of a rectangular verandah is 3m more than its breadth. the numerical value of its area is equal to the numerical value of its perimeter. Find the dimensions of the verandah:
1 x = 6; length = 5m and breadth = 3m
2 x = 3; length = 6m and breadth = 3m
3 x = 4; length = 4m and breadth = 2m
4 x = 5; length = 7m and breadth = 2m
Explanation:
x = 3; length = 6m and breadth = 3m Let the breadth of rectangular verandah = x therefore, length = x + 3 [According to given statement] area of the verandah = Perimeter of verandah l × b = 2(l + b) (3 + x) × x = 2(3 + x + x) 3x + x\(^{1}\) = 2(3 + 2x) x\(^{1}\) + 3x - 6 - 4x = 0 x\(^{1}\)- x - 6 = 0 x\(^{1}\)- 3x + 2x - 6 = 0 x(x - 3) + 2(x - 3) = 0 (x - 3) (x + 2) = 0 x = 3, x = - 2 Now, x = - 2 as dimension of the verandah cannot be in negative, \(\therefore\) x = 3 Length of rectangle = x + 3 = 3 + 3 = 6m Breadth of rectangle = x = 3m
09. MENSURATION
290114
The ______ of any polygon is the sum of the lengths of all the sides.
1 Volume
2 Area
3 Circumference
4 Perimete
Explanation:
Perimete The perimeter of any polygon is the sum of the lengths of all the sides. Example: In a square whose side is given as 2m, therefore, square has 4sides. Perimeter = 2 + 2 + 2 + 2 = 8m
09. MENSURATION
290115
A square shaped park ABCD of side 100m has two equal rectangular flower beds each of size 10m × 5m Length of the boundary of the remaining park is:
1 360m
2 400m
3 340m
4 460m
Explanation:
400m In order to find the length of the boundary of the remaining park, we add two flower beds each of length 10m and breadth 5m, then remaining park is shown below: Now, length of the boundary of the remaining park = Perimeter of remaining park = (90 + 5 + 10 + 95 + 90 + 5 + 10 + 95)m = 400m
09. MENSURATION
290116
If perimeter of a square is tripled, then area will be ........ of original area:
1 4 times
2 \(\frac{1}{4}\) times
3 9 times
4 \(\frac{1}{9}\) times
Explanation:
9 times S = 4SP\(_{\1}\) = 4×S' = 4S' P\(_{\1}\) = 3P thus, 4S' = 12SS = 3S A = S\(^{1}\)A = (S)\(^{1}\)A' = (3S)\(^{1}\)A' ?A' = 9A
290113
The length of a rectangular verandah is 3m more than its breadth. the numerical value of its area is equal to the numerical value of its perimeter. Find the dimensions of the verandah:
1 x = 6; length = 5m and breadth = 3m
2 x = 3; length = 6m and breadth = 3m
3 x = 4; length = 4m and breadth = 2m
4 x = 5; length = 7m and breadth = 2m
Explanation:
x = 3; length = 6m and breadth = 3m Let the breadth of rectangular verandah = x therefore, length = x + 3 [According to given statement] area of the verandah = Perimeter of verandah l × b = 2(l + b) (3 + x) × x = 2(3 + x + x) 3x + x\(^{1}\) = 2(3 + 2x) x\(^{1}\) + 3x - 6 - 4x = 0 x\(^{1}\)- x - 6 = 0 x\(^{1}\)- 3x + 2x - 6 = 0 x(x - 3) + 2(x - 3) = 0 (x - 3) (x + 2) = 0 x = 3, x = - 2 Now, x = - 2 as dimension of the verandah cannot be in negative, \(\therefore\) x = 3 Length of rectangle = x + 3 = 3 + 3 = 6m Breadth of rectangle = x = 3m
09. MENSURATION
290114
The ______ of any polygon is the sum of the lengths of all the sides.
1 Volume
2 Area
3 Circumference
4 Perimete
Explanation:
Perimete The perimeter of any polygon is the sum of the lengths of all the sides. Example: In a square whose side is given as 2m, therefore, square has 4sides. Perimeter = 2 + 2 + 2 + 2 = 8m
09. MENSURATION
290115
A square shaped park ABCD of side 100m has two equal rectangular flower beds each of size 10m × 5m Length of the boundary of the remaining park is:
1 360m
2 400m
3 340m
4 460m
Explanation:
400m In order to find the length of the boundary of the remaining park, we add two flower beds each of length 10m and breadth 5m, then remaining park is shown below: Now, length of the boundary of the remaining park = Perimeter of remaining park = (90 + 5 + 10 + 95 + 90 + 5 + 10 + 95)m = 400m
09. MENSURATION
290116
If perimeter of a square is tripled, then area will be ........ of original area:
1 4 times
2 \(\frac{1}{4}\) times
3 9 times
4 \(\frac{1}{9}\) times
Explanation:
9 times S = 4SP\(_{\1}\) = 4×S' = 4S' P\(_{\1}\) = 3P thus, 4S' = 12SS = 3S A = S\(^{1}\)A = (S)\(^{1}\)A' = (3S)\(^{1}\)A' ?A' = 9A
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