# A painting measures 12 inches by 16 inches and is surrounded by a frame of uniform width around the four edges. The perimeter of rectangle formed by the painting and its frame is 72 inches. What is the width of the frame?

Apr 22, 2018

2 inches.

#### Explanation:

Let $x$ be the frame's width. The width of the framed picture is $12 + 2 x$ and the height $16 + 2 x$ so the perimeter is

$72 = 2 \left(12 + 2 x\right) + 2 \left(16 + 2 x\right) = 56 + 8 x$

$16 = 8 x$

$x = 2$ inches

Check:  2 ( 16 + 20) = 72 quad sqrt