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20 Oct 2022, 06:34
Kudos
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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:
45%
(medium)
Question Stats:
71% (02:23) correct
29%
(02:32)
wrong
based on 52
sessions
History
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Not Attempted Yet
In the figure shown, if E and F are midpoints of the respective edges of the square ABCD, what percentage of the area of the square is common to the area of the triangle AEF?
(A) 33%
(B) 38%
(C) 48%
(D) 52%
(E) 62%
Attachment:
EG.jpeg [ 7.57 KiB | Viewed 2883 times ]
20 Oct 2022, 07:15
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Bunuel
Let, side of square = 4
Area of Square \(= 4^2 = 16\)
EF \(= \sqrt{2^2+2^2} = √8 = 2√2\)
AE = AF \(= \sqrt{4^2+2^2} = √20\)
i.e. ∆AEF has sides 2√2, √20, √20
Height drawn from point A on EF \(= \sqrt{20-2} = √18\)
ARea of ∆AEF \(= \frac{1}{2}*2√2*√18 = 6\)
Common area as percentage of area of square \(= \frac{6}{16}*100 = 37.5\)
Answer: Option B
