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