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    Question

    Find the area of maximum side of square that can be

    inscribed in a right angled triangle of side 15, 20 and 25 cm.
    A 1600/169 cm² Correct Answer Incorrect Answer
    B 3600/49 cm² Correct Answer Incorrect Answer
    C 200 cm² Correct Answer Incorrect Answer
    D 4900/169 cm² Correct Answer Incorrect Answer

    Solution

    Let the side of the square be a Then, AD = 15 – a and FC = 20 - a Area of Triangle ABC = 1/2 × Base × Height = 1/2 × 15 ×20 = 150 cm² Now, Area of Triangles ADE and EFC + Area of Square BDEF = Area of Triangle ABC ∴ 1/2 ×a × (15 - a) + 1/2 × a × (20 - a) + a² = 150 15a/2 - a²/2 + 10a - a²/2 + a² = 150 (15a+20a)/2 = 150 35a = 300 a = 300/35 = 60/7 cm Area of Square = 3600/49 cm²

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