Question

PLEASE HELP ASAP

EXTRA POINTS
Sheila places a 54 square inch photo behind a 12-inch-by-12-inch piece of matting.

The photograph is positioned so that the matting is twice as wide at the top and bottom as the sides.

Write an equation for the area of the photo in terms of x.

Answer 1

1. As you can see in the figure attached, the area of the photograph is:

A=LxW

A is the area of the photograph (A=54 in²).
L is the lenght of the photograph (L=12-4x).
W is the widht of the photograph (W=12-2x)

When you substitute these values into the formula A=LxW, you obtain:

A=LxW
54=(12-4x)(12-2x)

2. Now, you must apply the distributive property. Then:

54=144-24x-48x+8x²
8x²-72x+144-54=0

3. Therefore, you obtain a quadratic equation for the area of the photo:

8x²-72x+90=0

The answer is:

8x²-72x+90=0