Published by:
CGP EDU Academic Team
Published on: August 12, 2026
A right-angled isosceles triangle right-angled at origin has 2x + 3y = 6 as its base. Area of the triangle, is-
A
B
36/13
C
6
D
6 or 13
Text Solution
Verified by ExpertsThe correct answer is:
B
Let OAB be the right-angled isosceles triangle.
Let ∠ AOX = θ , Then
∠ BOY = θ (see fig.).
Let OA = OB = r. Then, we have
A ≡ (r cos θ , r sin θ ) and B ≡ (–r sin θ , r cos θ )
Since A and B both lie on the given line 2x + 3y = 6, therefore we have
2 cos θ + 3 sin θ = 
… (1)
and –2 sin θ + 3 cos θ = 
… (2)
squaring and adding equations (1) and (2), we have
2 2 + 3 2 = 
given r 2 = 
Hence, area of Δ OAB, is 
= 36/13.
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