SOLUTION: The outside of a picture frame measures 14 in by 20 in. 172 in^2 of the picture shows. Find the thickness of the frame.

Algebra ->  Length-and-distance -> SOLUTION: The outside of a picture frame measures 14 in by 20 in. 172 in^2 of the picture shows. Find the thickness of the frame.       Log On


   

Question 1059648: The outside of a picture frame measures 14 in by 20 in. 172 in^2 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!
Let +x+ = the thickness of the frame
+%28+14+-+2x+%29%2A%28+20+-+2x+%29+=+172+
+280+-+40x+-+28x+%2B+4x%5E2+=+172+
+4x%5E2+-+68x+%2B+280+=+172+
+4x%5E2+-+68x+%2B+108+=+0+
x%5E2+-+17x+%2B+27+=+0+
+x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-17+
+c+=+27+
+x+=+%28+-%28-17%29+%2B-+sqrt%28+%28-17%29%5E2+-+4%2A1%2A27+%29%29+%2F+%282%2A1%29+
+x+=+%28+17+%2B-+sqrt%28+289+-+108+%29%29+%2F+2+
+x+=+%28+17+%2B-+sqrt%28+181+%29%29+%2F+2+
+x+=+%28+17+-+13.4536+%29+%2F+2+ ( note the + sqrt gives too big a number )
+x+=+3.5464+%2F+2+
+x+=+1.7732+
The thickness of the frame is 1.7732 in.
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check:
+%28+14+-+2x+%29%2A%28+20+-+2x+%29+=+172+
+%28+14+-+2%2A1.7732+%29%2A%28+20+-+2%2A1.7732+%29+=+172+
+%28+14+-+3.5464+%29%2A%28+20+-+3.5464+%29+=+172+
+10.4536%2A16.4536+=+172+
+171.9993+=+172+
close enough