Question 45049
Let the width of the strip =x.

Then the width of the mat is the sum of the width of the painting and two times the width of the strip, or, W = 20 + 2x
The height of the mat is the sum of the height of the painting and two times the width of the strip, or H = 15 + 2x

The perimeter, P of the mat is twice the width (W) plus twice the height (H).
P = 2W + 2H
P = 2(20+2x) + 2(15+2x) Simplify.
P = 40+4x + 30+4x
P = 70+8x  But P = 102 ins.
70+8x = 102 Subtract 70 from both sides.
8x = 32 Divide both sides by 8.
x = 4 ins.

The width of the strip is 4 inches.