Question

The length of a rectangle is 13 centimeters less than its width. What are the dimensions of the rectangle if its area is 140 square centimeters?

Answer 1

Dimensions = 7 cm by 20 cm.

Explanation:

Let the length and width of the rectangle be L & W respectively.

Given the following data;

Area of rectangle = 140 cm²

L = W - 13

To find the dimensions of the rectangle;

The area of rectangle = L * W

Substituting into the above formula, we have;

140 = L * W

140 = (W - 13) * W

140 = W² - 13W

W² - 13W - 140 = 0

Solving the quadratic equation using factorization method;

Factors are -20 and 7

W² - 20W + 7W - 140 = 0

W(W - 20) + 7(W - 20) = 0

(W - 20)(W + 7) = 0

W - 20 = 0

W = 20

W + 7 = 0

W = -7

Thus, W = 20 or -7

But the width has to be positive, W = 20 centimeters.

Next, to find the length of rectangle

L = W - 13

L = 20 - 13

L = 7 centimeters.