(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 = \(\frac{1}{3}l \times b \times h\) = \(\frac{1}{3}(4.5) \times 2.5 \times 4 \) = \(15 m^{3}\).
