Question

The length of a rectangle is 5 ft less than three times the width, and the area of the rectangle is 28 ft2 . find the dimensions of the rectangle.

Answer 1

Let the width = w.
Then the length is 3w - 5.
The area = LW = 28

w(3w - 5) = 28

3w^2 - 5w = 28

3w^2 - 5w - 28 = 0

(3w + 7)(w - 4) = 0

3w + 7 = 0 or w - 4 = 0

w = -7/3 or w = 4

The width of a rectangle cannot be a negative number, so we discard w = -7/3.

The width is 4 ft.
The length is 3w - 5 = 3(4) - 5 = 12 - 5 = 7
The length is 7 ft

Answer: The dimensions are length 7 ft and width 4 ft.