Xavier Aptitude Test 2019 Paper

Question : 56 of 98

Marks: +1, -0

In the picture below, EFGH, ABCD are squares, and ABE, BCF, CDG, DAH are equilateral triangles. What is the ratio of the area of the square EFGH to that of ABCD?

$√2 +√3$
$√3 + 2$
$3 + √2$
$√2 + 2$
$1 +√3$

Validate

Solution:

Let

BE= x

and

EF =y

∴AB=x

and

EI=y/2

In right ΔBIE,

\cos15°={EI}/{EB}

⇒{√3+1}/{2√2}=y/{2x}

⇒y/x={√3+1}/√2

⇒y^2/x^2={4+2√3}/2=2+√3

∴ Ratio of the area of the square EFGH to that of ABCD

=(2+√3):1

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