If a rectangle is inscribed in an equilateral triangle of side length $2 \sqrt{2}$ as shown in the figure, then the square of the largest area of such a rectangle is _____.

Question

If a rectangle is inscribed in an equilateral triangle of side length 2√2 as shown in the figure, then the square of the largest area of such a rectangle is _____.

MARKS Content Team · Accepted Answer

Correct answer: 3. In ΔDBF, tan60°=2b/(2√2-ℓ) ⇒b=(√32√2-ℓ)/2 A=Area of rectangle =ℓ×b ⇒A=ℓ×√322√2-ℓ On differentiating, we get dA/(dℓ)=√322√2-ℓ-(ℓ·√3)/2=0 ⇒ℓ=√2 Now, A=ℓ×b =√2×√32√2=√3 ⇒A^2=3.

If a rectangle is inscribed in an equilateral triangle of side length $2 \sqrt{2}$ as shown in the figure, then the square of the largest area of such a rectangle is _____.

Solution

Relevant Questions

If a rectangle is inscribed in an equilateral triangle of side length 22 as shown in the figure, then the square of the largest area of such a rectangle is _____.

Solution

Relevant Questions

If a rectangle is inscribed in an equilateral triangle of side length $2 \sqrt{2}$ as shown in the figure, then the square of the largest area of such a rectangle is _____.