SOLUTION: a rectangular photograph 28 by 36 is mounted in the centre of a solid piece of matting which sticks out the same amount on all sides of the picture. the total area of the matted pi

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Question 1053998: a rectangular photograph 28 by 36 is mounted in the centre of a solid piece of matting which sticks out the same amount on all sides of the picture. the total area of the matted picture is to be doubled the area of the photograph find the width of the mat.
I do not understand the question itself...

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
It's worded kind of strangely
" the matted picture " that's the picture laid on top of the mat
" is double the area of the photograph "
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They shouldn't use "picture" and "photograph" to mean the same thing
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I think they just mean that the border around the photograph
is equal in area to the photograph itself
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Let +x+ = the width of the border around the photo
( border formed by the matt )
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The dimensions of the matt with the photo on it can
be expressed as:
+28+%2B+2x+ by +36+%2B+2x+
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" The total area of the matted picture is to
be doubled the area of the photograph"
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Using this statement, I can say:
+%28+28+%2B+2x+%29%2A%28+36+%2B+2x+%29+=+2%2A28%2A36+
+1008+%2B+72x+%2B+56x+%2B+4x%5E2+=+2016+
+4x%5E2+%2B+128x+-+1008+=+0+
+x%5E2+%2B+32x+-+252+=+0+
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Complete the square
+x%5E2+%2B+32x+%2B+%2832%2F2%29%5E2+=+252+%2B+%2832%2F2%29%5E2+
+x%5E2+%2B+32x+%2B+256+=+252+%2B+256+
+%28+x+%2B+16+%29%5E2+=+508+
+x+%2B+16+=+sqrt%28+508+%29+
+x+=+22.5389+-+16+
+x+=+6.5389+
The border is 6.5389 wide
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check answer:
+%28+28+%2B+2x+%29%2A%28+36+%2B+2x+%29+=+2%2A28%2A36+
+%28+28+%2B+2%2A6.5389+%29%2A%28+36+%2B+2%2A6.5389+%29+=+2%2A28%2A36+
+%28+28+%2B+13.0778+%29%2A%28+36+%2B+13.0778+%29+=+2016+
+41.0778%2A49.0778+=+2016+
+2016.008053+=+2016+
This is OK -error must be due to rounding off
Check my math, though, and
maybe get another opinion