# Quantitative Aptitude – Geometry – Mensuration – Points E, F, G, H lie on the sides

## Slot -1 – Quantitative Aptitude – Geometry – Mensuration – Points E, F, G, H lie on the sides

Points E, F, G, H lie on the sides AB, BC, CD, and DA, respectively, of a square ABCD. If EFGH is also a square whose area is 62.5% of that of ABCD and CG is longer than EB, then the ratio of length of EB to that of CG is?

a) 2 : 5

b) 4 : 9

c) 3 : 8

d) 1 : 3

Solution:

in triangle EBF ,EF^2=x^2+(a-x)^2

Ratio of Areas = AB^2:EF^2

1∶5/8=a^2: { x^2+(a-x)^2 }

8/5=a^2/(2x^2+a^2-2x )

16x^2+8a^2-16ax=5a^2
16x^2-16ax+3a^2=0
16x^2-12ax-4ax+3a^2=0

(4x-3a)(4x-a)=0
So 4x=a or 4x=3a

Thus CG=a-x=3x or 1/3 x
As CG > EB so CG = 3x

EB : CG = 1 : 3

Option d) 1:3 is correct.

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