Question

A rectangle has an area of 35.60 cm². When both the length and width of the rectangle are increased by 1.40 cm, the area of the rectangle becomes 55.62 cm². Calculate the length of the shorter of the two sides of the initial rectangle.

Answer 1

Area of the rectangle = A = 35.6 cm²

Length of the rectangle = L

Width of the rectangle = W

A = LW

LW = 35.6

The length and width of the rectangle are now increased by 1.4 cm each.

New area of the rectangle = A₁ = 55.62 cm²

New length of the rectangle = L₁ = L + 1.4

New width of the rectangle = W₁ = W + 1.4

A₁ = L₁W₁

55.62 = (L + 1.4)(W + 1.4)

55.62 = LW + 1.4L + 1.4W + 1.96

55.62 = 35.6 + 1.96 + 1.4(L + W)

L + W = 12.9

L = 12.9 - W

LW = 35.6

(12.9 - W)W = 35.6

12.9W - W² = 35.6

W² - 12.9W + 35.6 = 0

W = 8.9 cm or 4 cm

L = 12.9 - W

Therefore if W is 8.9 cm then L is 4 cm or if W is 4 cm then L is 8.9 cm.

Length of the shorter side = 4 cm