Question

A rectangle is inscribed in an equilateral triangle of side length '2a' units. Maximum area of this rectangle can be

• A. $\sqrt { 3 } a ^ { 2 }$
• B.
• C. a²
• D.

Answer 1

Answer: (D)

Answer 2

Let BD = x ⇒ BC₁ = (a - x) ⇒ BC = (a – x)tan $\frac { \pi } { 3 }$

Now area of rectangle ABCD,

∆ = (AB) (BC) = $2 \sqrt { 3 }$ × (a − x)

⇒ $\Delta \leq 2 \sqrt { 3 } \left( \frac { x + a - x } { 2 } \right) ^ { 2 }$

=(using A. M. ≥ G.M.)