(a) A rectangular field is l metres long and b metres wide. Its perimeter is 280 metres. If the length is two and a half times the breadth, find the values ...
Question 1 Report
(a) A rectangular field is l metres long and b metres wide. Its perimeter is 280 metres. If the length is two and a half times the breadth, find the values of l and b.
(b) The base of a pyramid is a 4.5 metres rectangle. The height of the pyramid is 4 metres. Calculate its volume.
Answer Details
(a) Let the length be \(l\) and the breadth \(b\). The perimeter is \(280\) m:
\[2(l + b) = 280 \;\Rightarrow\; l + b = 140\]
The length is two and a half times the breadth: \(l = 2.5b\). Substitute:
\[2.5b + b = 140 \;\Rightarrow\; 3.5b = 140 \;\Rightarrow\; b = 40\text{ m}, \quad l = 2.5(40) = 100\text{ m}\]
(b) Taking the base as a square of side \(4.5\) m and height \(4\) m, the volume of a pyramid is one-third of base area times height:
\[V = \frac13 \times (\text{base area}) \times h = \frac13 \times (4.5 \times 4.5) \times 4\]
\[= \frac13 \times 20.25 \times 4 = \frac{81}{3} = 27\text{ m}^3\]
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