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Thread: Pythagoras' theorem questions

  1. #1
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    Pythagoras' theorem questions

    Hello, would greatly appreciate if anybody could help with these questions...
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    Q1.


    pythag1.jpg

    Working so far:

    Triangle PQR has a hypotenuse of 9cm (6+3)
    Triangle PQS has a height of 6 cm.
    The two triangles share an angle both have right angles, an share a side (PQ) so, I think, are similar.
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    Q2.

    pythag2.jpg

    Working so far:

    AM^2 + CA^2 = CM^2
    AN^2 + AB^2 = BN^2


    Many thanks,

  2. #2
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    1) Yes, a right angle altitude leads to similarity. What does that do for you?
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

  3. #3
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    I can see now that there are three similar triangles:

    PQS, PQR and the smaller triangle SQR.
    Overall, we can tell that PQS has a height of 6 cm, PQR has a hypotenuse of 9cm and that the smaller triangle SQR has a Base of 3cm. So, between the three triangles we have the values for a hypotenuse, height and Base.

  4. #4
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    Quote Originally Posted by KMCC View Post
    I can see now that there are three similar triangles:

    PQS, PQR and the smaller triangle SQR.
    Overall, we can tell that PQS has a height of 6 cm, PQR has a hypotenuse of 9cm and that the smaller triangle SQR has a Base of 3cm. So, between the three triangles we have the values for a hypotenuse, height and Base.
    Keerect!

    r = PQ, p = RQ

    r^2 + p^2 = 81
    r^2 - x^2 = 36
    p^2 - x^2 = 9

    Plenty to solve for x, right?
    I'm just an imagination of your figment !

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