Question

The width of a rectangle is 10 feet shorter than its length. The area of the rectangle is 60 square feet. Find the length and width. Round your answer to the nearest tenth of a foot.

Answer 1

length: 14.2 ft; width 4.2 ft.

Explanation:

Let x represent the length of the rectangle in feet. Then x-10 represents the width, and the area is ...

area = length×width

60 = x(x -10) . . . . . substitute the expressions for area, length, width

60 = x² -10x

85 = x² -10x +25 . . . . add (10/2)² to complete the square

85 = (x -5)² . . . . . . . . . rewrite as a square

√85 = x -5 . . . . . . . . . take the square root. Only the positive root is useful for this problem

x = 5 + √85 ≈ 14.2

x-10 = 4.2

The length and width of the rectangle are 14.2 ft and 4.2 ft.