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20 Sep 2017, 01:53
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
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Question Stats:
84% (01:36) correct
16%
(01:50)
wrong
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In the above figure, PQRS is a square with side x + 4. Each of the four smaller squares has side of length 2. If the area of the shaded region is 48, what is the value of x?
(A) 1
(B) 4
(C) 4√2
(D) 8
(E) 12
Attachment:
2017-09-20_1020.png [ 4.39 KiB | Viewed 5537 times ]
20 Sep 2017, 05:52
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Bunuel
Width of the shaded portion = x-4-2-2=x (subtracting 2m from each side)
Length = 2
Area of each shaded rectangle = 2x
Area of 4 shaded rectangles = 4 x2x = 8x
Area of the middle square portion of shade = x^2
Total shaded area = x^2+8x = 48
Solving the quadratic equation, x =4
Answer B.
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Bunuel
Find numeric value for area of large square. Use (x + 4) to derive equation for the same area. Set them equal to solve for \(x\).
Numeric area
(Area of small squares) + (Area of shaded region) = Area of large square
Small square side = 2. Each small square's area = 4. Their total area = 4*4 = 16
Area of shaded region = 48
Area of large square = 16 + 48 = 64
Equation for same area
One side of large square = \((x + 4)\)
Equation for area of large square is
\((x + 4)^{2}\) = \(x^2 + 8x + 16\)
From above, numeric area of large square = 64. Set equation equal to numeric value:
\(x^2 + 8x + 16 = 64\)
\(x^2 + 8x - 48 = 0\)
\((x + 12)(x - 4) = 8\)
\(x\) cannot be negative
\(x = 4\)
ANSWER B
Edited to correct a really dumb mistake! Answer changed.
