PICTURE FRAMING The matting around the picture has a uniform width. How wide is the matting if its area equals the area of the picture? Round to the nearest of an inch.

Question

|---------------------------|
| <-------5in----------> |
| | wide | |
| | | |
| 4in long | |
| | | |
| | | |
| ---------------------- |
|---------------------------|

Answer 1

2w(5+2w) + 4(2w) = 20
10 w + 4 w^2 + 8 w = 20
4 w^2 + 18 w - 20 = 0
2 w^2 + 9 w - 10 = 0
w = [ -9 +/- sqrt(81+80) ]/4
w = [-9 +/- 12.7 ]/4
w = 0.922
check
0.922 * 8 + 0.922*10 + 4*0.922^2 = 19.99 yes