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 _____.

Aicharya · Accepted Answer

In &#916; D B F , tan 60 &#176; = 2 b 2 2 - &#8467; &#8658; b = 3 2 2 - &#8467; 2 A = Area of rectangle = &#8467; &#215; b &#8658; A = &#8467; &#215; 3 2 2 2 - &#8467; On differentiating, we get d A d &#8467; = 3 2 2 2 - &#8467; - &#8467; &#183; 3 2 = 0 &#8658; &#8467; = 2 Now, A = &#8467; &#215; b = 2 &#215; 3 2 2 = 3 &#8658; A 2 = 3 .

If a rectangle is inscribed in an equilateral triangle of side length 2 2 as shown in the figure, then the…

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