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# Triangle ABC above is an isosceles right triangle and triangle DEF abo

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Triangle ABC above is an isosceles right triangle and triangle DEF abo  [#permalink]

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18 Feb 2019, 12:23
2
00:00

Difficulty:

75% (hard)

Question Stats:

47% (02:01) correct 53% (01:27) wrong based on 30 sessions

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32323.jpg [ 9.93 KiB | Viewed 291 times ]

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 $$\sqrt{3}:2$$

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Re: Triangle ABC above is an isosceles right triangle and triangle DEF abo  [#permalink]

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18 Feb 2019, 22:49
1

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.

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Re: Triangle ABC above is an isosceles right triangle and triangle DEF abo  [#permalink]

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18 Feb 2019, 21:34
1
Attachment:
The attachment 32323.jpg is no longer available

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 $$\sqrt{3}:2$$

Attachments

Screen Shot 2019-02-18 at 10.20.15 PM.png [ 204.62 KiB | Viewed 250 times ]

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Re: Triangle ABC above is an isosceles right triangle and triangle DEF abo   [#permalink] 18 Feb 2019, 21:34
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