290109
Mark \((\checkmark)\) against the correct answer in the following: The area of a rectangular carpet is 120m² and its perimeter is 46m. The length of its diagonal is: Hint: l + b = 23 and lb = 120 Diagonal \(=\sqrt{\text{l}^2+\text{b}^2}=\sqrt{289}\) \(=\sqrt{17\times17}=17\)
1 15m
2 16m
3 17m
4 20m
Explanation:
17m Area of rectangular carpet = 120cm² Perimeter = 46m Now 2(l + b) = 46m \(\Rightarrow \text{l}+\text{b}=\frac{46}{2}=23\) and lb = 120 \(\therefore (\text{l}-\text{b})^2=(\text{l}+\text{b})^2-4\text{lb}\) \(=(23)^2-4\times120\) \(=529-480\) \(=49=(7)^2\) \(\therefore \text{l}-\text{b}=7\) and l + b = 23 Adding we get, 2l = 30 \(\Rightarrow \text{l}=\frac{30}{2}\) \(=15\) \(\therefore\) b = 23 - 15 = 8 Now diagonal \(=\sqrt{\text{l}^2+\text{b}^2}\) \(=\sqrt{(15)^2+(8)^2}\) \(=\sqrt{225+64}\) \(=\sqrt{289}\) \(=17\text{m}\)
09. MENSURATION
290110
Mark \((\checkmark)\) against the correct answer in the following: The diameter of a circle is 7cm, its circumference is:
290109
Mark \((\checkmark)\) against the correct answer in the following: The area of a rectangular carpet is 120m² and its perimeter is 46m. The length of its diagonal is: Hint: l + b = 23 and lb = 120 Diagonal \(=\sqrt{\text{l}^2+\text{b}^2}=\sqrt{289}\) \(=\sqrt{17\times17}=17\)
1 15m
2 16m
3 17m
4 20m
Explanation:
17m Area of rectangular carpet = 120cm² Perimeter = 46m Now 2(l + b) = 46m \(\Rightarrow \text{l}+\text{b}=\frac{46}{2}=23\) and lb = 120 \(\therefore (\text{l}-\text{b})^2=(\text{l}+\text{b})^2-4\text{lb}\) \(=(23)^2-4\times120\) \(=529-480\) \(=49=(7)^2\) \(\therefore \text{l}-\text{b}=7\) and l + b = 23 Adding we get, 2l = 30 \(\Rightarrow \text{l}=\frac{30}{2}\) \(=15\) \(\therefore\) b = 23 - 15 = 8 Now diagonal \(=\sqrt{\text{l}^2+\text{b}^2}\) \(=\sqrt{(15)^2+(8)^2}\) \(=\sqrt{225+64}\) \(=\sqrt{289}\) \(=17\text{m}\)
09. MENSURATION
290110
Mark \((\checkmark)\) against the correct answer in the following: The diameter of a circle is 7cm, its circumference is:
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09. MENSURATION
290109
Mark \((\checkmark)\) against the correct answer in the following: The area of a rectangular carpet is 120m² and its perimeter is 46m. The length of its diagonal is: Hint: l + b = 23 and lb = 120 Diagonal \(=\sqrt{\text{l}^2+\text{b}^2}=\sqrt{289}\) \(=\sqrt{17\times17}=17\)
1 15m
2 16m
3 17m
4 20m
Explanation:
17m Area of rectangular carpet = 120cm² Perimeter = 46m Now 2(l + b) = 46m \(\Rightarrow \text{l}+\text{b}=\frac{46}{2}=23\) and lb = 120 \(\therefore (\text{l}-\text{b})^2=(\text{l}+\text{b})^2-4\text{lb}\) \(=(23)^2-4\times120\) \(=529-480\) \(=49=(7)^2\) \(\therefore \text{l}-\text{b}=7\) and l + b = 23 Adding we get, 2l = 30 \(\Rightarrow \text{l}=\frac{30}{2}\) \(=15\) \(\therefore\) b = 23 - 15 = 8 Now diagonal \(=\sqrt{\text{l}^2+\text{b}^2}\) \(=\sqrt{(15)^2+(8)^2}\) \(=\sqrt{225+64}\) \(=\sqrt{289}\) \(=17\text{m}\)
09. MENSURATION
290110
Mark \((\checkmark)\) against the correct answer in the following: The diameter of a circle is 7cm, its circumference is:
290109
Mark \((\checkmark)\) against the correct answer in the following: The area of a rectangular carpet is 120m² and its perimeter is 46m. The length of its diagonal is: Hint: l + b = 23 and lb = 120 Diagonal \(=\sqrt{\text{l}^2+\text{b}^2}=\sqrt{289}\) \(=\sqrt{17\times17}=17\)
1 15m
2 16m
3 17m
4 20m
Explanation:
17m Area of rectangular carpet = 120cm² Perimeter = 46m Now 2(l + b) = 46m \(\Rightarrow \text{l}+\text{b}=\frac{46}{2}=23\) and lb = 120 \(\therefore (\text{l}-\text{b})^2=(\text{l}+\text{b})^2-4\text{lb}\) \(=(23)^2-4\times120\) \(=529-480\) \(=49=(7)^2\) \(\therefore \text{l}-\text{b}=7\) and l + b = 23 Adding we get, 2l = 30 \(\Rightarrow \text{l}=\frac{30}{2}\) \(=15\) \(\therefore\) b = 23 - 15 = 8 Now diagonal \(=\sqrt{\text{l}^2+\text{b}^2}\) \(=\sqrt{(15)^2+(8)^2}\) \(=\sqrt{225+64}\) \(=\sqrt{289}\) \(=17\text{m}\)
09. MENSURATION
290110
Mark \((\checkmark)\) against the correct answer in the following: The diameter of a circle is 7cm, its circumference is: