Question 385217
The length of a picture is one inch less than twice its width. the frame around the picture has a uniform width of two inches and an area of 96 square inches. what are the dimensions of the picture?
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width of picture = w
length = 2w-1
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Area of picture = w(2w-1)
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uniform width of 2 in.surrounding the picture
so width will be w+4
length = (2w-1)+4=2w+3
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Area of picture + area frame =(w+4)(2w+3)
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(Area of picture + area frame)-area of picture= area of frame
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(w+3)(2w+3)-w(2w-1)=96
2w^2+9w+9-2w^2+w=96
10w+9=96
-9   -9
10w=87
/10
{{{(highlight(w=8.7))}}}cm the width
Length = 2w-1= 2*8.7-1
Length =17.4-1
Length{{{(highlight(l=16.4))}}}cm