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Legs of a right triangle scaled: new hypotenuse or original legs

This type of question, asked 2 times: CDS 2 2019, CDS 2 2023. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2019

    83
    The hypotenuse of a right-angled triangle is 10 cm and its area is 24 cm2\text{cm}^2. If the shorter side is halved and the longer side is doubled, the new hypotenuse becomes

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  2. Question 2

    CDS 2 2023

    59
    The hypotenuse AC of a right-angled ABC is 353\sqrt{5} cm. If AB is doubled and BC is tripled such that ABC remains a right-angled triangle, the hypotenuse becomes 15 cm. What is AB + BC equal to ?

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