SOLUTION: you place a mat around a 25 inch by 21 inch painting as shown. the mat is twice as wide at the left and right of the painting as it is in top and bottom of the painting. the area o
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-> SOLUTION: you place a mat around a 25 inch by 21 inch painting as shown. the mat is twice as wide at the left and right of the painting as it is in top and bottom of the painting. the area o
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Question 1012150: you place a mat around a 25 inch by 21 inch painting as shown. the mat is twice as wide at the left and right of the painting as it is in top and bottom of the painting. the area of the mat is 714 square inches. how wide is the mat at the left and right of the painting? at the too amd bottom of the painting? Answer by macston(5194) (Show Source):
You can put this solution on YOUR website! W=width of painting=25 in
H=height of painting=21 in
Area of painting and mat=(25 in)(21 in)+(714 in^2)
Area of painting and mat=525 in^2 + 714 in^2
Area of painting and mat=1239 in^2
Let x=mat width at top, then:
mat width at bottom=x
mat width at left=2x
mat width at right=2x
.
Width of mat=2x+W+2x=W+4x
Height of mat=x+H+x=H+2x
Area of mat and painting=(W+4x)(H+2x)
1239 in^2=(25+4x)(21+2x)
1239=525+50x+84x+8x^2
1239=8x^2+134x+525
0=8x^2+134x-714
0=(8x-34)(x+21)
8x-34=0 -OR- x+21=0
8x=34 -OR- x=-21
x=4.25
ANSWER 1: The width of the mat at the top and bottom is 4.25 in.
.
Width on sides=2x=2(4.25)=8.5 in
ANSWER 2: The width of the mat on each side is 8.5 in.
.
