CAT 2018 Slot 1 QA Question 10: 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 o

Question

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 o

Accepted Answer

Let the side of square ABCD be s, and let $EB = x$.
Since EFGH is a square formed with one vertex on each side, the corresponding adjacent cut on the next side is $CG = s - x$.
The side of EFGH has length
$\sqrt{x^{2} + (s - x)^{2}}$
The area ratio is 62.5%, i.e. $\dfrac{5}{8}$.
$\dfrac{x^{2} + (s -

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