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16 Feb 2018, 02:45
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
72% (02:14) correct
28%
(02:22)
wrong
based on 115
sessions
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The short diagonal of a rhombus is three-quarters the length of the long diagonal. If the perimeter of the rhombus is 20, then what is the area of the rhombus?
A 14
B 15
C 24
D 25
E 40
A 14
B 15
C 24
D 25
E 40
16 Feb 2018, 02:56
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Tridhipal
Perimeter = 20
so the sides of rhombus are 5 each. Each sides forms a triangle i.e 3,4,5 triplet.
So (3,4,5) , (3,4,5) , (3,4,5) , (3,4,5)
D1 = 3+3
D2 = 4+4
area = 1/2 D1 D2 = 1/2 x 6 x 8 = 24
(C) imo
16 Feb 2018, 05:00
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Tridhipal
You are given that perimeter is 20 and you know that each side of a rhombus is equal. So each side would be 5.
Now knowing that the hypotenuse is 5 doesn't necessarily mean that the other two sides will be 3 and 4. They could very well be 2 and \(\sqrt{21}\) or infinite other values.
But there is one more data point - the short diagonal is (3/4)th the length of the long diagonal. So the two are in the ratio 3:4. This means the ratio of half of their lengths (the legs of the right triangle) will also be 3:4. So we know that the two legs will be 3 and 4 giving the hypotenuse as 5.
Area of rhombus = 4* Area of triangle = 4 * (1/2)*3*4 = 24
Answer (C)
