Question

1.3.29

X

A rectangular painting measures 10 inches by

16 inches and contains a frame of uniform

width around the four edges. The perimeter of

the rectangle formed by the painting and its

frame is 76 inches. Determine the width of the

frame.

X

What is the width of the frame?

inch(es)

Answer 1

The width of the frame is 3 inches

Explanation:

We are told that the inner rectangle is 10 inches by 16 inches.

It means the outer rectangle has to be (L = 10 + 2x) by (W = 16 + 2x),

Where x represents the width of the frame.

The perimeter of the frame is given by; p = 2L + 2W

p = 2(10+2x) + 2(16+2x)

We are given perimeter, P = 76

Thus;

2(10 + 2x) + 2(16 + 2x) = 76

Divide both sides by 2 to give;

(10+2x) + (16+2x) = 38

(10+16) + (2x+2x) = 38

4x = 38 - 26

4x = 12

x = 12/4 = 3

The width of the frame is x = 3 inches