SOLUTION: A solar collector is 2.5 m long by 2.0 m wide. It is held in place by a frame of uniform width around its outside edge. If the exposed collector is 4 m2, what is the width of the f

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Question 102565: A solar collector is 2.5 m long by 2.0 m wide. It is held in place by a frame of uniform width around its outside edge. If the exposed collector is 4 m2, what is the width of the frame to the nearest tenth of a centimeter?
Answer by josmiceli(6786) About Me  (Show Source):
You can put this solution on YOUR website!
2%2A2.5+=+5
If the exposed area is 4, then the area of the
frame is 1
Call the width of the frame x
Then 2.5x+%2B+2.5x+%2B+x%282+-+2x%29+%2B+x%282+-+2x%29+=+1
5x+%2B+2x%282+-+2x%29+=+1
5x+%2B+4x+-+4x%5E2+=+1
4x%5E2+-+9x+%2B+1+=+0
This is in the form
ax%5E2+%2B+bx+%2B+c+=+0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-9%29+%2B-+sqrt%28+%28-9%29%5E2-4%2A4%2A1+%29%29%2F%282%2A4%29+
x+=+%289+%2B-+sqrt%2881+-+16%29%29+%2F+8
x+=+%289+%2B-+sqrt%2865%29%29+%2F+8
x+=+%289+%2B-+8.062%29+%2F+8
x+=+%289+-+8.062%29+%2F+8 gives the only reasonable answer
x+=+.117 m, or
x+=+11.7 cm answer