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Isosceles right triangle with a given perimeter: find its area

The same question, asked 2 times: CDS 1 2022*, CDS 1 2026. Every wording below, oldest first.

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  1. Question 1

    CDS 1 2022

    75
    If the perimeter of an isosceles right triangle is 4(2+2)4(2 + \sqrt{2}) cm, then what is its area in square cm?

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  2. Question 2

    CDS 1 2026

    51
    The perimeter of a right-angled isosceles triangle is 20 units. If α\alpha is the area of the triangle, then

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