JEE Mains · Maths · STD 12 - 6. Application of derivatives
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 \(....\)
- A \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(C) \(3\)
Step-by-step Solution
Detailed explanation
In \(\triangle \mathrm{DBF}\) \(\tan 60^{\circ}=\frac{2 \mathrm{~b}}{2 \sqrt{2}-\ell} \Rightarrow \mathrm{b}=\frac{\sqrt{3}(2 \sqrt{2}-\ell)}{2}\) \(\mathrm{~A}=\text { Area of rectangle }=\ell \times \mathrm{b}\) \(\mathrm{A}=\ell \times \frac{\sqrt{3}}{2}(2 \sqrt{2}-\ell)\)…
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