SOLUTION: a matte uniform width is to be placed around a painting so that the area of the matted surface is twice the area of the picture. If the outside of the matte are 40cm and 60cm, find

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Question 994258: a matte uniform width is to be placed around a painting so that the area of the matted surface is twice the area of the picture. If the outside of the matte are 40cm and 60cm, find the width of the matte.
i have the answer to the question i just dont know how to show my work doing it.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Let the width of the matte be xcm.
the outside dimensions of the matte are 40 by 60 cm
the length of the picture will be 60+-2x+ ... ( x cm on each side, so 2x)
the width of the picture will be 40-2x
.
the area of the picture+%2B+matte+=+60%2A40+=+2400cm%5E2
the area of the picture+=+%2860-2x%29%2840-2x%29
.
the area of the%28+picture+%2B+matte%29++-+%28area_+of_+picture%29+=+2%2860-2x%29%2840-2x%29
.
=>2400-%2860-2x%29%2840-2x%29=+2%2860-2x%29%2840-2x%29
2400=+3%2860-2x%29%2840-2x%29
800=+2400-120x-80x%2B4x%5E2
4x%5E2-200x%2B1600=0
x%5E2-50x%2B400=0
x%5E2-40x-10x%2B400=0
x%28x-40%29-10%28x-40%29=0
%28x-10%29%28x-40%29+=0
x=+10 or x=40
x=10 satisfies the equation, so the width of matte is 10cm