SOLUTION: A picture frame is 18 inches by 14 inches. If 221 square inches of picture shows, find the width of the frame, assuming the distance is equal all the way around.

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Question 736721: A picture frame is 18 inches by 14 inches. If 221 square inches of picture shows, find the width of the frame, assuming the distance is equal all the way around.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The area of the picture plus the frame is
+18%2A14+=+252+ in2
+252+-+221+=+31+ in2
If +x+ = the width of the frame,
+A+=+18x+%2B+18x+%2B+%28+14+-+2x+%29%2Ax+%2B+%28+14+-+2x+%29%2Ax+
+A+=+36x+%2B+2x%2A%28+14+-+2x+%29+
+A+=+-4x%5E2+%2B+28x+%2B+36x+
+A+=+-4x%5E2+%2B+64x+
+-4x%5E2+%2B+64x+-+31+=+0+
Use quadratic formula
+x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-4+
+b+=+64+
+c+=+-31+
+x+=+%28-64+%2B-+sqrt%28+64%5E2+-+4%2A%28-4%29%2A%28-31%29+%29%29+%2F+%282%2A%28-4%29%29+
+x+=+%28-64+%2B-+sqrt%28+4096+-+496+%29%29+%2F+%28-8%29+
+x+=+%28-64+%2B-+sqrt%28+3600+%29%29+%2F+%28-8%29+
+x+=+%28+-64+%2B+60+%29+%2F+%28-8%29+
+x+=+1%2F2+
and, the other answer is:
+x+=+%28+-64+-+60+%29+%2F+%28-8%29+
+x+=+15.5+ ( impossible for width of frame )
The width of the frame is 1/2 in
check:
+A+=+36x+%2B+2x%2A%28+14+-+2x+%29+
+A+=+36%2A%281%2F2%29+%2B+2%2A%281%2F2%29%2A%28+14+-+2%2A%281%2F2%29+%29+
+A+=+18+%2B+1%2A%28+13+%29+
+A+=+31+
OK