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Largest square inscribed in a triangle

This type of question, asked 2 times: CDS 1 2024, CDS 2 2026. All 2 questions below, oldest first.

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  1. Question 1

    CDS 1 2024

    13
    ABC is a right-angled triangle, right-angled at B such that AB = 6 cm and BC = 8 cm. What is the perimeter of the square inscribed in the triangle ABC with maximum area ?

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  2. Question 2

    CDS 2 2026

    75
    A square of maximum area is inscribed in an equilateral triangle. If the side of the triangle is equal to (6+43)(6 + 4\sqrt{3}) cm, then what is the area of the square ?

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