Question

Tara places a picture in a picture frame. The width of the picture is x inches, and the length of the picture is 2 inches more than the width. The frame is 1 inch wide on all sides. The perimeter of the outside of the picture frame is 28 inches. Tara writes the equation below to find the width, in inches, of the picture. 2(x + 2) + 2(x + 4) = 28 What is the width, in inches, of the picture?

Answer 1

Refer to the diagram shown below.

The dimensions of the outside of the picture rame are:
Width = x + 1 + 1 = x + 2 inches
Length = (x+2) + 1 + 1 = x + 4 inches.

The perimeter of the outside of the picture frame is 28 inches.
Therefore
2(x + 2) + 2(x+4) = 28

Solve for x.
2x + 4 + 2x + 8 = 28
4x + 12 = 28
4x = 16
x = 4 inches

Answer: 4 inches