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?
3
4
6
8
9
A
3
B
4
C
9
D
8
E
6
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Solution
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Let the width of the border be ′x′ inch.
Therefore area of shaded region =(10+2x)(8+2x)−10×8
⇒144=80+20x+16x+4x2−80
⇒4x2+36x−144=0⇒x2+9x−36=0
⇒x2+12x−3x−36=0⇒(x+12)(x−3)=0
∴x=−12,, 3 (neglecting negative value.)
∴ Therefore width of border is 3 inches.
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