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5 June, 21:35

Using the altitude theorem. I have a triangle, the altitude is 20. a is 25 but there's no b. Just the sum of a and b which is x. How do I solve this problem?

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  1. 5 June, 22:30
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    Step-by-step explanation:

    We're given a right triangle with an altitude h = 20 that divides the hypotenuse into two segments a and b, and given a = 25 and a + b = x.

    The altitude theorem states that h = sqrt (a*b), or equivalently that h^2 = a*b. We already know what a and h are; now let's solve for b.

    a + b = x

    a + b - a = x - a

    b = x - a

    So then

    h^2 = a*b

    h^2 = a * (x - a)

    h^2 = ax - a^2

    20^2 = 25x - 25^2

    400 = 25x - 625

    400 + 625 = 25x - 625 + 625

    1025 = 25x

    1025/25 = 25x/25

    x = 41

    Now we plug this back into our equation for b.

    b = x - a

    b = 41. - 25

    b = 16

    We can verify that this is the correct answer using the altitude theorem.

    h^2 = a*b

    20^2 = 25*16

    400 = 400
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