The length of a rectangle is 4 inches less than twice its width. If the area of the rectangle is 70 square inches, what are its dimensions?

Please help.

Area of a rectangle = l * w

l = length

w = width

In this problem,

w = x

l = 2x - 4

Area = 70 in^2.

Plug these numbers into the area formula above.

70 = (2x - 4)x.

Distribute the x

70 = 2x^2 - 4x.

Subtract 70 from both sides

0 = 2x^2 -4x - 70

Factor the expression on the right side

0 = 2(x - 7) (x + 5) .

Set each term equal to zero

2 = 0.

x + 5 = 0.

Subtract 5 from each side

x = -5. Side lengths cannot he negative so we need to check the last term

x - 7 = 0

Add 7 to each side

x = 7

The width = 7 and we know that the length = 2(width) - 4, therefore,

l = 2(7) - 4

Simplify the expression

l = 10

The length is 10 inches and the width is 7 inches

step-by-step explanation: