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
Explanation:
y > x
Side of smaller square = x2+y2 ∴ Area of smaller square = (x2 + y2)
Side of bigger square = (x + y) ∴ Area of bigger square = (x + y)2
By the given condition,
⇒ x2 + y2 = 62.5% of (x + y)2
⇒ x2 + y2 = 5/8 (x + y)2
⇒ 8x2 + 8y2 = 5x2 + 5y2 + 10xy
⇒ 3x2 + 3y2 - 10xy = 0
⇒ 3xy2 -10xy + 3 = 0
⇒ xy = 10±102-4×3×36 = 10±86 = 9/3 of 1/3
As y > x, x/y < 1
∴ x : y = 1 : 3
Hence, option (d).
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