Question

# A rectangle has an area of 35.60 cm2. When both the length and width of the...

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.

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

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