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Geometry

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Geometry

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3 squares are overlapped one another with the same center shown as above. If all points intersected are midpoints, what fraction of the area of the largest square is the area of the region shaded?

A. 1/2 B. 1/3 C. 1/4 D. 1/5 E. 2/3

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Each triangle in the figure above is an isosceles right triangle with sides 1, 1 and √2.
Shaded region = 4 triangles.
Largest square = 16 triangles.
Thus:
(shaded region)/(largest square) = 4/16 = 1/4.

The correct answer is C.

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Post
rawat2583 wrote:
3 squares are overlapped one another with the same center shown as above. If all points intersected are midpoints, what fraction of the area of the largest square is the area of the region shaded?

A. 1/2 B. 1/3 C. 1/4 D. 1/5 E. 2/3

We can let the side of the largest square be 10. Thus the side of second largest square is 10/2 x √2 = 5√2 and the side of the smallest square is (5√2)/2 x √2 = 5. Now, the area of the largest, second largest and the smallest squares are 10^2 = 100, (5√2)^2 = 50 and 5^2 = 25, respectively. The shaded area is the difference between the area of the second largest and smallest squares, so it’s 50 - 25 = 25. Thus the fraction of the largest square is shaded is 25/100 = 1/4.

Answer: C

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scott@targettestprep.com



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