\({3}\text{x} + {4}\) Length of side of square \(= \frac{3\text{x}}{4} + {1}\) Perimeter of a square = 4 × side \( = {4} \times \big(\frac{3\text{x}}{4} + {1}\big)\) = 3x + 4 So, perimeter of square with side \(\big(\frac{3\text{x}}{4} + {1}\big) \text{ is } ({3}\text{x} + {4})\)
09. MENSURATION
290106
The perimeter of a rectangular garden is 30 feet. If its length is 6 feet, what is its width?
1 9 feet
2 10 feet
3 18 feet
4 21 feet
5 24 feet
Explanation:
9 feet The perimeter of a shape is the distance around it. In particular, the perimeter of a rectangle is given by the formula P = 2W + 2L. Substitute the correct values of the variables into this formula (P = 30 and L = 6) and then solve for the width W: 30 = 2W + 2(6) 30 = 2W + 12 18 = 2W W = 9 Therefore, the width of the garden is 9 feet.
09. MENSURATION
290107
The perimeter of a rectangle is twice the ........ of length and breadth of the rectangle:
1 difference
2 sum
3 product
4 None
Explanation:
sum The perimeter of the rectangle is the sum of all sides that is 2 × length + 2 × breadth So, we can say that the perimeter of a rectangle is twice the sum of length and breadth.
09. MENSURATION
290108
The length of a rectangle is three tmies of its width. If the length of the diagonal is \(8\sqrt{10}\text{m}\), then the perimeter of the rectangle is:
1 \(15\sqrt{10}\text{m}\)
2 \(16\sqrt{10}\text{m}\)
3 \(24\sqrt{10}\text{m}\)
4 \(64\text{m}\)
Explanation:
\(64\text{m}\) Let us consider a rectangle ABCD. Also, let us assume that the width of the rectangle, i.e., BC be × m. It is given that the length is three times width of the rectangle. Therefore, length of the rectangle, i.e., AB = 3x m Now, AC is the diagonal of rectangle. In right angled triangle ABC. \(\text{AC}^{2}=\text{AB}^{2}+\text{BC}^{2}\) \(\big(8\sqrt{10}\big)^{2}=\big(3\text{x}\big)^{2}+\text{x}^{2}\) \(640=9\text{x}^{2}+\text{x}^{2}\) \(640=10\text{x}^{2}\) \(\text{x}^{2}=\frac{64}{10}=64\) \(\text{x}=\sqrt{64}=8\text{m}\) Thus, breadth of the rectangle = x = 8m Similarly, length of the rectangle = 3x = 3 × 8 = 24m Perimeter of the rectangle = 2(Length + Breadth) = 2(24 + 8) = 2 × 32 = 64m
\({3}\text{x} + {4}\) Length of side of square \(= \frac{3\text{x}}{4} + {1}\) Perimeter of a square = 4 × side \( = {4} \times \big(\frac{3\text{x}}{4} + {1}\big)\) = 3x + 4 So, perimeter of square with side \(\big(\frac{3\text{x}}{4} + {1}\big) \text{ is } ({3}\text{x} + {4})\)
09. MENSURATION
290106
The perimeter of a rectangular garden is 30 feet. If its length is 6 feet, what is its width?
1 9 feet
2 10 feet
3 18 feet
4 21 feet
5 24 feet
Explanation:
9 feet The perimeter of a shape is the distance around it. In particular, the perimeter of a rectangle is given by the formula P = 2W + 2L. Substitute the correct values of the variables into this formula (P = 30 and L = 6) and then solve for the width W: 30 = 2W + 2(6) 30 = 2W + 12 18 = 2W W = 9 Therefore, the width of the garden is 9 feet.
09. MENSURATION
290107
The perimeter of a rectangle is twice the ........ of length and breadth of the rectangle:
1 difference
2 sum
3 product
4 None
Explanation:
sum The perimeter of the rectangle is the sum of all sides that is 2 × length + 2 × breadth So, we can say that the perimeter of a rectangle is twice the sum of length and breadth.
09. MENSURATION
290108
The length of a rectangle is three tmies of its width. If the length of the diagonal is \(8\sqrt{10}\text{m}\), then the perimeter of the rectangle is:
1 \(15\sqrt{10}\text{m}\)
2 \(16\sqrt{10}\text{m}\)
3 \(24\sqrt{10}\text{m}\)
4 \(64\text{m}\)
Explanation:
\(64\text{m}\) Let us consider a rectangle ABCD. Also, let us assume that the width of the rectangle, i.e., BC be × m. It is given that the length is three times width of the rectangle. Therefore, length of the rectangle, i.e., AB = 3x m Now, AC is the diagonal of rectangle. In right angled triangle ABC. \(\text{AC}^{2}=\text{AB}^{2}+\text{BC}^{2}\) \(\big(8\sqrt{10}\big)^{2}=\big(3\text{x}\big)^{2}+\text{x}^{2}\) \(640=9\text{x}^{2}+\text{x}^{2}\) \(640=10\text{x}^{2}\) \(\text{x}^{2}=\frac{64}{10}=64\) \(\text{x}=\sqrt{64}=8\text{m}\) Thus, breadth of the rectangle = x = 8m Similarly, length of the rectangle = 3x = 3 × 8 = 24m Perimeter of the rectangle = 2(Length + Breadth) = 2(24 + 8) = 2 × 32 = 64m
\({3}\text{x} + {4}\) Length of side of square \(= \frac{3\text{x}}{4} + {1}\) Perimeter of a square = 4 × side \( = {4} \times \big(\frac{3\text{x}}{4} + {1}\big)\) = 3x + 4 So, perimeter of square with side \(\big(\frac{3\text{x}}{4} + {1}\big) \text{ is } ({3}\text{x} + {4})\)
09. MENSURATION
290106
The perimeter of a rectangular garden is 30 feet. If its length is 6 feet, what is its width?
1 9 feet
2 10 feet
3 18 feet
4 21 feet
5 24 feet
Explanation:
9 feet The perimeter of a shape is the distance around it. In particular, the perimeter of a rectangle is given by the formula P = 2W + 2L. Substitute the correct values of the variables into this formula (P = 30 and L = 6) and then solve for the width W: 30 = 2W + 2(6) 30 = 2W + 12 18 = 2W W = 9 Therefore, the width of the garden is 9 feet.
09. MENSURATION
290107
The perimeter of a rectangle is twice the ........ of length and breadth of the rectangle:
1 difference
2 sum
3 product
4 None
Explanation:
sum The perimeter of the rectangle is the sum of all sides that is 2 × length + 2 × breadth So, we can say that the perimeter of a rectangle is twice the sum of length and breadth.
09. MENSURATION
290108
The length of a rectangle is three tmies of its width. If the length of the diagonal is \(8\sqrt{10}\text{m}\), then the perimeter of the rectangle is:
1 \(15\sqrt{10}\text{m}\)
2 \(16\sqrt{10}\text{m}\)
3 \(24\sqrt{10}\text{m}\)
4 \(64\text{m}\)
Explanation:
\(64\text{m}\) Let us consider a rectangle ABCD. Also, let us assume that the width of the rectangle, i.e., BC be × m. It is given that the length is three times width of the rectangle. Therefore, length of the rectangle, i.e., AB = 3x m Now, AC is the diagonal of rectangle. In right angled triangle ABC. \(\text{AC}^{2}=\text{AB}^{2}+\text{BC}^{2}\) \(\big(8\sqrt{10}\big)^{2}=\big(3\text{x}\big)^{2}+\text{x}^{2}\) \(640=9\text{x}^{2}+\text{x}^{2}\) \(640=10\text{x}^{2}\) \(\text{x}^{2}=\frac{64}{10}=64\) \(\text{x}=\sqrt{64}=8\text{m}\) Thus, breadth of the rectangle = x = 8m Similarly, length of the rectangle = 3x = 3 × 8 = 24m Perimeter of the rectangle = 2(Length + Breadth) = 2(24 + 8) = 2 × 32 = 64m
\({3}\text{x} + {4}\) Length of side of square \(= \frac{3\text{x}}{4} + {1}\) Perimeter of a square = 4 × side \( = {4} \times \big(\frac{3\text{x}}{4} + {1}\big)\) = 3x + 4 So, perimeter of square with side \(\big(\frac{3\text{x}}{4} + {1}\big) \text{ is } ({3}\text{x} + {4})\)
09. MENSURATION
290106
The perimeter of a rectangular garden is 30 feet. If its length is 6 feet, what is its width?
1 9 feet
2 10 feet
3 18 feet
4 21 feet
5 24 feet
Explanation:
9 feet The perimeter of a shape is the distance around it. In particular, the perimeter of a rectangle is given by the formula P = 2W + 2L. Substitute the correct values of the variables into this formula (P = 30 and L = 6) and then solve for the width W: 30 = 2W + 2(6) 30 = 2W + 12 18 = 2W W = 9 Therefore, the width of the garden is 9 feet.
09. MENSURATION
290107
The perimeter of a rectangle is twice the ........ of length and breadth of the rectangle:
1 difference
2 sum
3 product
4 None
Explanation:
sum The perimeter of the rectangle is the sum of all sides that is 2 × length + 2 × breadth So, we can say that the perimeter of a rectangle is twice the sum of length and breadth.
09. MENSURATION
290108
The length of a rectangle is three tmies of its width. If the length of the diagonal is \(8\sqrt{10}\text{m}\), then the perimeter of the rectangle is:
1 \(15\sqrt{10}\text{m}\)
2 \(16\sqrt{10}\text{m}\)
3 \(24\sqrt{10}\text{m}\)
4 \(64\text{m}\)
Explanation:
\(64\text{m}\) Let us consider a rectangle ABCD. Also, let us assume that the width of the rectangle, i.e., BC be × m. It is given that the length is three times width of the rectangle. Therefore, length of the rectangle, i.e., AB = 3x m Now, AC is the diagonal of rectangle. In right angled triangle ABC. \(\text{AC}^{2}=\text{AB}^{2}+\text{BC}^{2}\) \(\big(8\sqrt{10}\big)^{2}=\big(3\text{x}\big)^{2}+\text{x}^{2}\) \(640=9\text{x}^{2}+\text{x}^{2}\) \(640=10\text{x}^{2}\) \(\text{x}^{2}=\frac{64}{10}=64\) \(\text{x}=\sqrt{64}=8\text{m}\) Thus, breadth of the rectangle = x = 8m Similarly, length of the rectangle = 3x = 3 × 8 = 24m Perimeter of the rectangle = 2(Length + Breadth) = 2(24 + 8) = 2 × 32 = 64m
