SOLUTION: A picture 9 inches by 21 inches is to be mounted on a piece of mat board so that there is an even amount of mat all around the picture. How wide will the border be if the area of t

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Question 411189: A picture 9 inches by 21 inches is to be mounted on a piece of mat board 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 325 sq in?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The dimensions of the picture + mat is
9+%2B+2x x 21+%2B+2x where x is the
width of the border on each side
given:
%289+%2B+2x%29%2A%2821+%2B+2x%29+=+325 in2
+189+%2B+42x+%2B+18x+%2B+4x%5E2+=+325
4x%5E2+%2B+60x+-+136+=+0
x%5E2+%2B+15x+-+34+=+0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+15
c+=+-34
x+=+%28-15+%2B-+sqrt%28+15%5E2+-+4%2A1%2A%28-34%29+%29%29%2F%282%2A1%29+
x+=+%28-15+%2B-+sqrt%28+225+%2B+136+%29%29+%2F+2+
x+=+%28-15+%2B-+sqrt%28+361%29%29+%2F+2+
x+=+%28-15+%2B+19%29%2F2
x+=+2
The border is 2 in wide
check answer:
%289+%2B+2x%29%2A%2821+%2B+2x%29+=+325
%289+%2B+2%2A2%29%2A%2821+%2B+2%2A2%29+=+325
%289+%2B+4%29%2A%2821+%2B+4%29+=+325
13%2A25+=+325
325+=325
OK