Question 45049: All paints with watercolors on a sheet of paper 20 ijn wide by 15 in high. He then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. The perimeter of the mat is 102 in. How wide is the strip of the mat showing around the picture??
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! 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.
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