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Altitude to the hypotenuse cuts it into two given segments: find the altitude

The same question, asked 4 times: CDS 2 2018*, CDS 1 2021*, CDS 1 2022*, CDS 2 2022. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2018

    97
    In the figure given below, ABC is a triangle with AB perpendicular to BC. Further BD is perpendicular to AC. If AD = 9 cm and DC = 4 cm, then what is the length of BD ?

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  2. Question 2

    CDS 1 2021

    79
    ABCABC is a triangle right angled at AA and ADAD is perpendicular to BCBC. If BD=8BD = 8 cm and DC=12.5DC = 12.5 cm, then what is ADAD equal to?

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  3. Question 3

    CDS 1 2022

    12
    The perpendicular dropped from a vertex of a right-angled triangle upon the hypotenuse divides it into two segments of lengths 9 units and 16 units respectively. What is the length of the perpendicular?

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  4. Question 4

    CDS 2 2022

    76
    Triangle ABC is right-angled at A and AD is perpendicular to BC. If BD = 7.5 cm and DC = 10 cm, then what is AD equal to ?

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