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

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## CAT 2018 – Slot 1 - Mensuration - Question 4 - Points E, F, G, H lie on the sides

Q. 4: 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
1. 2 :5
2. 4 :9
3. 3 :8
4. 1 :3 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

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