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PS Rectangle Area

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Senior | Next Rank: 100 Posts
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by Shadow » Tue Jul 10, 2007 10:37 pm
Please find attached the file containing the figure.

A rectangular picture is surrounded by a boarder, as shown in the figure. Without the boarder the length of the picture is twice its width. If the area of the boarder is 196 square inches, what is the length,in inches,of the picture,excluding the boarder?

A.10
B.15
C.30
D.40
E.60

I proceeded in this way...

For the picture

let l be the length and w be the width.
Given l=2w

Area of the boarder = 196
(2w+4)(w+4)=196
After exapnsion it becomes
w^2+6w-90=0

Its not possible to factorise the above equation....Could anyone please help me out?
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by givemeanid » Wed Jul 11, 2007 5:37 am
Area of the boarder = 196
(2w+4)(w+4)=196

That is not the area of the border. That is area of entire outer rectangle.

Area of border = Area of outer rectangle - Area of inner rectangle
196 = (2w+4)(w+4) - 2w*w
12w = 180
w = 15
l = 30
So It Goes
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by gmat_perfect » Mon Jun 14, 2010 1:52 am
Without border,
The length of the picture = 2X
The width of the picture = X
Area = 2x^2

With border,
The length of the picture = 2x+2+2=2x+4
The width of the picture = x+2+2=x+4
So, area with border =(2x+4)(x+4)

Accordingly,
196 =(2x+4)(x+4) -2x^2
=> 196 =2x^2+4x+8x+16-2x^2
=> 196 =12x+16
=> 12x=180
=> X=180/12 =15

So, the length of the picture without t border =2X=2×15=30
Answer is C.
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