SOLUTION: Bill has an 8 inch × 10 inch picture of his family. He wants to hang it in a frame that encloses an area of 224 in square 2. How wide must the picture border x be to cover this are

Algebra ->  Conversion and Units of Measurement -> SOLUTION: Bill has an 8 inch × 10 inch picture of his family. He wants to hang it in a frame that encloses an area of 224 in square 2. How wide must the picture border x be to cover this are      Log On


   

Question 1111828: Bill has an 8 inch × 10 inch picture of his family. He wants to hang it in a frame that encloses an area of 224 in square 2. How wide must the picture border x be to cover this area

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Frame? Picture Border? Not clear. One might almost believe you meant that the total area for frame and picture should be 224 square inches.

%288%2B2x%29%2810%2B2x%29=224
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2%2A2%284%2Bx%29%285%2Bx%29=4%2A56
%284%2Bx%29%285%2Bx%29=56
The two factors only differ by 1, and are 7%2A8=56.

highlight%28highlight%28x=3%29%29.

Uniform frame width surrounding the picture is 3 inches.

Answer by ikleyn(52896) About Me  (Show Source):
You can put this solution on YOUR website!
.
The problem can be easily solved MENTALLY. 

Since the frame is of uniform width, the difference of exterior dimensions of the frame is the same as the difference of dimensions 

of the picture, i.e. 10 - 8 = 2 inches.


So, to solve the problem, you need to decompose the number of 224 into the product of two factors with the difference of 2 between them.  It is


224 = 225 - 1 = 15%5E2-1 = (15-1)*(15+1) = 14*16.


From this decomposition,  14 = 8 + 2w  and hence  w = %2814-8%29%2F2 = 3 inches.

Solved.

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