Area of a rectangle = l * w
A = Area of a rectangle
l = length
w = width
In our problem,
l = x
w = x - 3
A = 180 square inches
Plug our numbers into the area formula of a rectangle
180 square inches = x(x-3)
Distribute the x into (x-3)
180 square inches = x^2 - 3x
subtract 180 from both sides
0 = x^2 - 3x -180.
Factor the express on the left side of the equation
0 = (x-15) (x+12).
Set each term equal to zero and solve for x
x+12 = 0.
Subtract 12 from both sides
x = -12 <--- lengths of a rectangle cannot be negative, therefore, we need to check the other term we factored.
set x-15 equal to zero
x-15 = 0.
Add 15 to both sides
x = 15.
We know l = x so now we know that the length i = 15 inches.
We also know that the width = length - 3
w = 15 - 3
w = 12
The width is 12 inches and the length is 15 inches
