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13 Oct 2019, 08:24
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B
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Difficulty:
55%
(hard)
Question Stats:
63% (03:04) correct
38%
(02:50)
wrong
based on 64
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Find the area of the shaded region if ABCD is a square of side 4 units and E is the midpoint of side BC.
A. 2
B. 8/3
C. 4
D. 16/3
E. None of these
A. 2
B. 8/3
C. 4
D. 16/3
E. None of these
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13 Oct 2019, 08:39
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Dillesh4096
\(\triangle {CFE}\) and \(\triangle {DFA}\) are similar so when we draw an altitude passing through F, the height or altitude of both triangles will be in ratio 2/4 or 1/2.
Thus if smaller altitude is x, bigger altitude = 2x and \(x+2x=4..x=\frac{4}{3}\)
Area of ABED = \(\frac{4+2}{2}*4=12\)=area of shaded region \(+4+\frac{16}{3}\)..
area of shaded region =\(12-\frac{28}{3}=\frac{36-28}{3}=8/3\)
B
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13 Oct 2019, 09:39
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Dillesh4096
Let the coordinates of point A be (0,0)
Coordinates of point E = (4,2)
Equation of line AC : y = x
Equation of line DE passing through (0,4) & (4,2): y-4 = (-2/4)x: y = 4 - x/2
Coordinates of point F (intersection point of AC & DE)
y = x = 4 - x/2
x = 8/3 = y
Coordinates of point F = (8/3,8/3)
Using discriminant method,
Area of triangle AFE = 1/2 (32/3 - 16/3) = 8/3
IMO B
