Question

The perimeter of a rectangle is 104 m and its area is 640 m². Find its length and breadth.

Answer 1

Let the length and the breadth of the rectangle be x m and y m.

Perimeter = 2(x + y) m

∴ 104 = 2(x + y)

x + y = 52

y = 52 – x

Area = 640 m²

∴ xy = 640

x(52 – x) = 640

x² – 52x + 640 = 0

x² – 32x – 20x + 640 = 0

x(x – 32) – 20(x – 32) = 0

(x – 32)(x – 20) = 0

x = 32, 20

When x = 32, y = 52 – 32 = 20

When x = 20, y = 52 – 20 = 32

Thus, the length and breadth of the rectangle are 32 m and 20 m.