Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The maximum area of the rectangle whose sides pass through the angular points of a given the rectangle is of sides a and b is
Text Solution
Verified by ExpertsThe correct answer is:
C
Let ABCD be the given rectangle of sides a and b and EFGH be any rectangle, whose sides pass through A, B, C, D
A = area EFGH = (b sin θ + a cos θ ) (a sin θ + b cos θ )
= ab + (a 2 + b 2 ) sin θ cos θ
dA/d θ = (a 2 + b 2 ) cos 2 θ so dA/d θ = 0
⇒ θ = π /4
⇒ 
= – 2 (a 2 + b 2 ) sin 2 θ , so 
< 0
Hence A max = (1/2) (a + b) 2 .
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