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Difficulty:
45%
(medium)
Question Stats:
71% (02:53) correct
29%
(02:58)
wrong
based on 250
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In the square above, 12w = 3x = 4y. What fractional part of the square is shaded?
A. 2/3
B. 14/25
C. 5/9
D. 11/25
E. 3/7
Attachment:
1.gif [ 1.83 KiB | Viewed 9151 times ]
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PareshGmat
Joined: 27 Dec 2012
Last visit: 10 Jul 2016
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Concentration: General Management, Technology
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Posts: 1,531
12w = 3x = 4y
x = 4w &
y = 3w
Area of square \(= (5w)^2 = 25w^2\) .............. (1)
Area of un shaded region (4 right triangles) \(= \frac{1}{2} w * 4w + \frac{1}{2} 2 w^2 + \frac{1}{2} 4w * 3w + \frac{1}{2} w * 4w\)
\(= 2w^2 + w^2 + 6w^2 + 2w^2 = 11w^2\) ............. (2)
Area of shaded region \(= 25w^2 - 11w^2 = 14w^2\)
Fraction \(= \frac{14}{25}\)
Answer = B
x = 4w &
y = 3w
Area of square \(= (5w)^2 = 25w^2\) .............. (1)
Area of un shaded region (4 right triangles) \(= \frac{1}{2} w * 4w + \frac{1}{2} 2 w^2 + \frac{1}{2} 4w * 3w + \frac{1}{2} w * 4w\)
\(= 2w^2 + w^2 + 6w^2 + 2w^2 = 11w^2\) ............. (2)
Area of shaded region \(= 25w^2 - 11w^2 = 14w^2\)
Fraction \(= \frac{14}{25}\)
Answer = B
General Discussion
Bunuel
Take W=1 then
x=4
y=3
Area of 4 triangles= 11
Area of square =5^2=25
Portion shaded =25-11/25=14/25
Ans B
Posts: 609
area of shaded region = area of square-area of remaining bits
area of square = 25w^2
area of remaining bits = 1/2(2W^2+4w^2+4w^2+12w^2)=11W^2
area of shaded region = 25w^2-11w^2 =14w^2
fraction = 14/25
area of square = 25w^2
area of remaining bits = 1/2(2W^2+4w^2+4w^2+12w^2)=11W^2
area of shaded region = 25w^2-11w^2 =14w^2
fraction = 14/25
Great question!
First we calculate total area of the square.
Then deduct sum of areas of 4 triangles.
Let's calculate areas in terms of w:
Area of the square = 5w * 5w = 25w^2
Sum of Area of 4 triangles = 1/2 * (2W^2+2*4w^2+12w^2)=11W^2
Area of the shaded region = 14w^2
Ratio = 14/25
First we calculate total area of the square.
Then deduct sum of areas of 4 triangles.
Let's calculate areas in terms of w:
Area of the square = 5w * 5w = 25w^2
Sum of Area of 4 triangles = 1/2 * (2W^2+2*4w^2+12w^2)=11W^2
Area of the shaded region = 14w^2
Ratio = 14/25
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