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20 Dec 2012, 05:33
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A
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A border of uniform width is placed around a rectangular photograph that measures 8 inches by 10 inches. If the area of the border is 144 square inches, what is the width of the border, in inches?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 9
(A) 3
(B) 4
(C) 6
(D) 8
(E) 9
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20 Dec 2012, 05:42
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Walkabout
Consider the diagram below:
The area of just the photograph is 8*10=80 square inches.
The area of the photograph with the border is \((10+2x)(8+2x)=4x^2+36x+80\) square inches.
The difference is 144 square inches, thus \((4x^2+36x+80)-80=144\) --> \(4x^2+36x-144=0\) --> \(x^2+9x-36=0\) --> \((x-3)(x+12)=0\) --> \(x=3\).
Answer: A.
Attachment:
photograph.png [ 5.15 KiB | Viewed 289929 times ]
27 Aug 2014, 02:27
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Refer diagram below:
photograph.png [ 3.89 KiB | Viewed 250358 times ]
Area of multi-coloured shaded region is given = 144
Area of each square (Yellow) = \(x^2\) ; No. of squares = 4
Area of rectangle (pink) = 10x ; No. of rectangle (pink) = 2
Area of rectangle (blue) = 8x ; No. of rectangle (pink) = 2
Setting up the equation
\(4x^2 + 20x + 16x = 144\)
\(x^2 + 9x - 36 = 0\)
x = 3
Answer = A
Attachment:
photograph.png [ 3.89 KiB | Viewed 250358 times ]
Area of each square (Yellow) = \(x^2\) ; No. of squares = 4
Area of rectangle (pink) = 10x ; No. of rectangle (pink) = 2
Area of rectangle (blue) = 8x ; No. of rectangle (pink) = 2
Setting up the equation
\(4x^2 + 20x + 16x = 144\)
\(x^2 + 9x - 36 = 0\)
x = 3
Answer = A
