Theory question 105
Mensuration of Plane Shapes(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 its breadth, find the values of l and b.
(b) The base of a pyramid is a 4.5 m by 2.5 m rectangle. The height of the pyramid is 4 m. Calculate its volume.
Show the model answer
Model answer
(a) 2(l + b) = 280 → l + b = 140, and l = 2.5b. So 3.5b = 140 → b = 40 m and l = 100 m.
(b) V = ⅓ × base area × height = ⅓ × 4.5 × 2.5 × 4 = 15 m3.
Explanation
Substitute l = 2.5b into the perimeter equation.