SOLUTION: The outside of a mosaic mirror frame measures 14 in. by 20 in., and 160 in^2 of mirror shows. Find the width of the frame.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The outside of a mosaic mirror frame measures 14 in. by 20 in., and 160 in^2 of mirror shows. Find the width of the frame.      Log On


   

Question 890279: The outside of a mosaic mirror frame measures 14 in. by 20 in., and 160 in^2 of mirror shows. Find the width of the frame.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+14%2A20+=+280+ in2 of total area
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The width is uniform all around, I assume
Let +x+ = the width of the frame
+%28+14+-+2x+%29%2A%28+20+-+2x+%29+=+160+
+280+-+40x+-+28x+%2B+4x%5E2+=+160+
+4x%5E2+-+68x+%2B+120+=+0+
+x%5E2+-+17x+%2B+30+=+0+
Use quadratic formula to solve:
x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-17+
+c+=+30+
x+=+%28+-%28-17%29+%2B-+sqrt%28+%28-17%29%5E2+-+4%2A1%2A30+%29%29+%2F+%282%2A1%29+
x+=+%28+17+%2B-+sqrt%28+289+-+120+%29%29+%2F+2+
x+=+%28+17+%2B-+sqrt%28+169+%29%29+%2F+2+
+x+=+%28+17+-+13+%29+%2F+2+
+x+=+4%2F2+
+x+=+2+
Note that I used the negative square root of +169+
because if I used the positive square root, I would
get +x+=+15+, which makes no sense
So, the width of the frame is 2 inches
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check:
+%28+14+-+2x+%29%2A%28+20+-+2x+%29+=+160+
+%28+14+-+2%2A2+%29%2A%28+20+-+2%2A2+%29+=+160+
+10%2A16+=+160+
OK