SOLUTION: A picture 16 inches by 25 inches is to be mounted on a piece of matboard so that there is an even amount of mat all around the picture. How wide will the border be if the area of

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Question 221212: A picture 16 inches by 25 inches is to be mounted on a piece of matboard so that there is an even amount of mat all around the picture. How wide will the border be if the area of the mounted picture is 792 square inches?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width of the border around
the picture = x
I can express the width of the mat as
16+%2B+x and the length as
25+%2B+x
%2816+%2B+x%29%2A%2825+%2B+x%29+=+792
400+%2B+25x+%2B+16x+%2B+x%5E2+=+792
x%5E2+%2B+41x+-+392+=+0
Solve using quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-41+%2B-+sqrt%28+41%5E2-4%2A1%2A%28-392%29+%29%29%2F%282%2A1%29+
x+=+%28-41+%2B-+sqrt%28+1681+%2B+1568+%29%29%2F2+
x+=+%28-41+%2B-+sqrt%28+3249+%29%29%2F2+
x+=+%28-41+%2B-+57%29%2F2+
x+=+16%2F2
x+=+8 (reject the negative solution)
The border will be 8 in wide
check answer:
%2816+%2B+x%29%2A%2825+%2B+x%29+=+792
%2816+%2B+8%29%2A%2825+%2B+8%29+=+792
24%2A33+=+792
792+=+792
OK