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26 August, 19:30

In right triangle qrs, angle r is a right angle. The altitude rt is drawn to hypotenuse qs. If qr is 20 and qs is 25 then find the length of qt.

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Answers (2)
  1. 26 August, 19:40
    0
    length of qt = 16

    Step-by-step explanation:

    Given in the question that qrs is a right angle triangle,

    where qr = 20

    sr = ?

    qs = 25

    qt = ?

    1) Find sr

    hypotenuse² = base² + height²

    sq² = sr² + rq²

    25² - 20² = sr²

    sr = √25² - 20²

    sr = 15

    2)

    When altitude rt is drawn to hypotenuse qs, it divides the triangle qrs into

    two right angle triangle, rtq and rts.

    Δrtq

    height = rt

    base = tq = 25 - x

    hypotenuse = qt = 20

    Δrts

    height = rt

    base = ts = x

    hypotenuse = sr = 15

    These both triangle shares same altitude that is rt

    So, by using pythagorus theorem

    Δ rtq Δ rts

    hypotenuse² - base² = height² = hypotenuse² - base²

    20² - (25 - x) ² = 15² - x²

    400 - (625 + x² - 50x) = 225 - x²

    400 - 625 - x² + 50x = 225 - x²

    -225 - x² + 50x - 225 + x² = 0

    -450 + 50 x = 0

    50x = 450

    x = 450/50

    x = 9

    base of Δ rtq = tq = 25 - x

    tq = 25 - 9

    tq = 16
  2. 26 August, 19:53
    0
    The length of qt is 15

    Step-by-step explanation:

    According to Pythagorean Theorem

    c² = a² + b²

    c² - a² = b²

    25² - 20² = b²

    625 - 400 = b²

    225 = b²

    Taking square root on both sides

    b = 15
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