zeza wrote: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
OA: A
Total area = photograph + border = (8*10) + 144 = 224.
Since the border SURROUNDS the photograph -- whose dimensions are 8 x 10 -- we get:
(border width + 8 + border width)(border width + 10 + border width) = 224.
We can plug in the answers for the width of the border.
Answer choice C: 6
(6 + 8 + 6)(6 + 10 + 6) = 20*22 = 440.
The area is almost double 224, so the width of the border must be much smaller.
Answer choice A: 3
(3 + 8 + 3)(3 + 10 + 3) = 14*16 = 224.
Success!
The correct answer is
A.
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