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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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