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

Question

32323.jpg 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

alldaytestprep · Answer

See attachment for answer. Thanks!

EgmatQuantExpert · Answer

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

https://e-gmat.com/blogs/wp-content/uploads/2016/12/Geometry-Ability-Quiz-4-e1480581478957.png

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

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