Question 307423: a matte of 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 dimensions of the matte are 40cm and 60cm, find the width of the matte.
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! a matte of 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 dimensions of the matte are 40cm and 60cm, find the width of the matte.
Let the width of the matte be x cm
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 + matte = 60*40 = 2400 sq. cm
the area of the picture = (60-2x)(40-2x)
.
the area of the picture + matte - area of picture = 2(60-2x)(40-2x).
.
2400-(60-2x)(40-2x)= 2(60-2x)(40-2x)
2400= 3(60-2x)(40-2x)
800= 2400-120x-80x+4x^2
4x^2-200x+1600=0
x^2-50x+400=0
x^2-40x-10x+400=0
x(x-40)-10(x-40)=0
(x-10)(x-40) =0
x= 10 or 40
x=10 satisfies the equation
the width of matte is 10 cm
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