Question

The perimeter of a rectangle is 54 cm. The area of the same rectangle is 176 cm². What are the dimensions of the rectangle

Answer 1

Let L and W represent the length and width of the rectangle.

Because the perimeter of the rectangle is 54 and opposite sides of a rectangle are congruent, then 2L + 2W = 54. Dividing by 2, L + W = 27. L = 27 - W.

The area of a rectangle is the product of its length and width.
L*W = 176.

Substituting for L with L = 27 - W, L*W = 176 becomes (27 - W)*(W) = 176. Collecting all terms on one side of the equation gives W² - 27 W + 176 = 0. This factors as (W - 16)(W - 11) = 0.
By the Zero Product Property, W - 16 = 0 or W - 11 = 0, giving W = 16 or W = 11.
Back substituting for W = 16 in L = 27 - W, L = 27 - 16 = 11. Similar substitution for W = 11 gives L = 16. The dimensions of the rectangle are 11 and 16.