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Right triangle from perimeter and area or sum of legs: use (a+b)^2 = c^2 + 4 x area

This type of question, asked 2 times: CDS 1 2023, CDS 2 2025. All 2 questions below, oldest first.

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  1. Question 1

    CDS 1 2023

    88
    The perimeter and the area of a right-angled triangle are 36 cm and 54 square cm respectively. What is the length of the hypotenuse ?

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  2. Question 2

    CDS 2 2025

    67
    ABCABC is a triangle right angled at BB. Further, (AB+BC)(AB + BC) exceeds ACAC by 10 units. If the perimeter of the triangle is 60 units, then what is the area of the triangle?

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