(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.
Explanation
(a) Perimeter of a rectangle = 2(l + b)
\(2l + 2b = 280\)
But l = 2.5b,
\(2(2.5b) + 2b = 280 \implies 7b = 280\)
\(b = 40 m\)
\(\therefore l = 2.5(40) \)
= \(100 m\)
(b) Volume of pyramid = \(\frac{1}{3}l \times b \times h\)
= \(\frac{1}{3}(4.5) \times 2.5 \times 4 \)
= \(15 m^{3}\).