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18 Feb 2019, 12:23
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
58% (01:49) correct
42%
(01:36)
wrong
based on 108
sessions
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Triangle ABC above is an isosceles right triangle and triangle DEF above is an equilateral triangle with height EG. What is the ratio of the area of ABC to the area of DEF ?
(1) The ratio of BC to EG is 1:1
(2) The ratio of AC to DF is \(\sqrt{3}:2\)
18 Feb 2019, 22:49
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Solution
Given:
- • ABC is an isosceles right triangle
• DEF is an equilateral triangle with height EG.
To find:
- • The ratio of area of ABC to the area of DEF.
Approach and Working:
We know that ABC is an isosceles right triangle.
- • Hence, AC = BC = a
• Therefore, area of triangle ABC = 1/2 x a x a
Also, DEF is an equilateral triangle.
If we assume the length if each side is equal to b, then height of the triangle is √3/2 x b and the area of the triangle is √3/4 x b^2.
So, area of ABC: area of DEF = 1/2 a^2: √3/4 b^2
Hence, if we know either the individual values of a and b, or the ratio of a and b, then we can determine our answer.
Analysing Statement 1
As per the information given in statement 1, BC: EG = 1: 1
- • Or, a: √3/2 b = 1: 1
From this equation, we can determine the ratio of a and b.
Hence, statement 1 is sufficient to answer the question.
Analysing Statement 2
As per the information given in statement 2, AC: DF = √3: 2
- • Or, a: b = √3: 2
Hence, statement 2 is sufficient to answer the question.
Hence, the correct answer is option D.
Answer: D
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alldaytestprep
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Expert reply
18 Feb 2019, 21:34
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SajjadAhmad
See attachment for answer. Thanks!
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Screen Shot 2019-02-18 at 10.20.15 PM.png [ 204.62 KiB | Viewed 5236 times ]
