A rectangle has a length, 3x+7, and a width of x+5. The area of the rectangle is 128 square inches. What is the length of the rectangle in inches?

First, we know the formula for area is:

Area = Length * Width

Therefore, 128 = (3x+7) (x+5)

We can use the F. O. I. L method to multiply

- First: (3x * x) = 3x²

-Outer: (3x*5) = 15x

-Inner: (7*x) = 7x

-Last: (7*5) = 35

Now we add the sum → 3x² + 15x + 7x + 35 → 3x² + 22x + 35

3x² + 22x + 35 = 128

3x² + 22x - 93 = 0

Now you have to factor to solve for the x value.

(3x + 31) (x-3)

x = 3 & x = - 31/3

The negative value is eliminated because u can't have a negative length.

The length is 3x+7

L = 3 (3) + 7

L = 9+7

L = 16