Discussion

Explanation:

Let the side of equilateral triangle be a. Hence, perimeter = 3a.

Let the sides of the rectangle be x and 3x. Hence, perimeter = 8x

Given, 3a + 8x = 90   …(1)

Also given, R = T2

⇒ x × 3x = 34a22

⇒ 16x2 = a4

⇒ a2 = 4x

Substituting x in (1)

⇒ 3a + 2a2 = 90

⇒ 2a2 + 3a – 90 = 0

⇒ a = -15/2 or 6 (-ve value will be rejected) 

∴ x = a24 = 9

∴ Longer side of the rectangle = 3x = 27.

Hence, option (a).

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