Area 3

A rectangle has a perimeter of 16 inches and an area of 12 square inches. Find the length and the width of the rectangle.

Solution: Let the length and width of the rectangle be L in and W in.

Given, Perimeter = 16 inches

⇒ 2(L + W) = 16

⇒ L + W = 8

⇒ W = 8 – L

Also, Area = 12

⇒ LxW = 12 square inches

⇒ Lx(8 – L) = 12; since, W = 8 – L

⇒ 8L – L² = 12

⇒ L² --8L + 12 = 0

⇒ L² --6L –2L + 12 = 0

⇒ L(L -- 6) –2(L -- 6) = 0

⇒ (L--6)(L--2) = 0

⇒ L = 6; L = 2

when L = 2, W = 8 - 2 = 6 and

when L = 6, W = 8 - 6 = 2

Hence, the length and width are 6 inch and 2 inch