Question

A rectangular painting measures 13 inches by 18 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 78 inches. Determine the width of the frame.

Answer 1

2 inches

Explanation:

We can find the border width by writing an equation for the perimeter of the framed picture. The frame adds 2x to each picture dimension, so the perimeter of the painting and frame is ...

P = 2(L +W)

78 = 2((18 +2x) +(13 +2x)) . . . . use the known dimensions for length, width

39 = 31 +4x . . . . . divide by 2 and simplify

8 = 4x . . . . . . . . subtract 31

2 = x . . . . . . . divide by 4

The width of the frame is 2 inches.