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In the figure, ABCD is a rectangle. Points E and F cut the
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19 Mar 2019, 05:39
19 Mar 2019, 05:39
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86% (01:39) correct
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In the figure, ABCD is a rectangle. Points E and F cut the sides BC and CD of the rectangle respectively such that EC = 3, FC = 4, and AD = 12, and the areas of the crossed and the shaded regions in the figure are equal. Which one of the following equals the perimeter of rectangle ABCD ?
(A) 42
(B) 50
(C) 56
(D) 64
(E) 72
Re: In the figure, ABCD is a rectangle. Points E and F cut the
[#permalink]
13 Apr 2020, 10:37
13 Apr 2020, 10:37
Expert Reply
Area of triangle = \(1/2*(Base)*(Height)\)
Area of triangle AEC= Area of triangle ACF(given)
\((1/2)*3*(CD)= (1/2)*4*12\)
\(CD= (4*12*2)/ (2*3)\)
\(CD= 96/6 = 16\)
Also, AD=12 (given)
Hence, Perimeter=\(2*(AD+CD) = 2*(16+12) =56\)
Hence Answer is C
Area of triangle AEC= Area of triangle ACF(given)
\((1/2)*3*(CD)= (1/2)*4*12\)
\(CD= (4*12*2)/ (2*3)\)
\(CD= 96/6 = 16\)
Also, AD=12 (given)
Hence, Perimeter=\(2*(AD+CD) = 2*(16+12) =56\)
Hence Answer is C
Re: In the figure, ABCD is a rectangle. Points E and F cut the
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07 Jun 2021, 01:02
07 Jun 2021, 01:02
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