SOLUTION: The outside of a picture frame measures 14 in by 19 in. 150 in squared of the picture shows. Find the thickness of the frame.

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Question 1056747: The outside of a picture frame measures 14 in by 19 in. 150 in squared of the picture shows. Find the thickness of the frame.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I'll assume a uniform thickness all around
+%28+14+-+2x+%29%2A%28+19+-+2x+%29+=+150+
+266+-+38x+-+28x+%2B+4x%5E2+=+150+
+4x%5E2+-+66x+%2B+116+=+0+
+2x%5E2+-+33x+%2B+58+=+0++
Use the quadratic formula
+x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+2+
+b+=+-33+
+c+=+58+
+x+=+%28+-%28-33%29+%2B-+sqrt%28+%28-33%29%5E2+-+4%2A2%2A58+%29%29+%2F+%282%2A2%29+
+x+=+%28+33+%2B-+sqrt%28+1089+-+464+%29%29+%2F+4+
+x+=+%28+33+%2B-+sqrt%28+625+%29%29+%2F+4+
+x+=+%28+33+-+25+%29+%2F+4+ ( using the positive square root gives an impossible answer )
+x+=+8%2F4+
+x+=+2+
The thickness of the frame is 2 inches
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check:
+%28+14+-+2x+%29%2A%28+19+-+2x+%29+=+150+
+%28+14+-+2%2A2+%29%2A%28+19+-+2%2A2+%29+=+150+
+%28+14+-+4+%29%2A%28+19+-+4+%29+=+150+
+10%2A15+=+150+
+150+=+150+
OK