Geometry

Okay, this is going to be confusing to describe, so please bear with me (have paper and pencil ready).

There is a right triangle with an altitude of 12. The line of the altitude splits the base into two segments, x and x+7. One leg of the right triangle is y, which is closest to the segment x. The other leg is z, which is closest to segment x+7.

We have to figure out what the values of x, y, and z are. Thanks for helping me out!

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  1. Since this is a right triangle, you can use the Pythagorean theorem several times to solve for all unknowns. Let y be the side adjacent to the segment x and z be the side adjacent to x+7. The length of the hypotenuse, c, is 2x + 7.

    Then you have
    x^2 + 144 = y^2
    (x+7)^2 + 144 = z^2
    y^2 + z^2 = (2x+7)^2

    There are three equations in three unknowns, so with a bit of messy algebra, x, y anx z can all be determined.
    Try x=9, y=15 and z = 20. All three triangles are of the 3,4,5 variety

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  2. There is a right triangle with an altitude of 12. The line of the altitude splits the base into two segments, x and x+7. One leg of the right triangle is y, which is closest to the segment x. The other leg is z, which is closest to segment x+7.

    We have to figure out what the values of x, y, and z are. Thanks for helping me out!

    The altitude to the hypotenuse of a right triangle creates two similar triangles, each similar to the original right triangle and to each other.

    The altitude to the hypotenuse of a right triangle is the geometric mean between the segments of the hypotenuse created by the point where the altitude intersects the hypotenuse or h^2 = x(x+7).

    x/12 = 12/(x + 7) yields x^2 = 7x - 144 = 0

    Using the quadratic formula

    x [-7+/-sqrt(49 + 576)]/2

    x = [-7+/-25]/2 = 18/2 = 9.

    Then, y = sqrt(9^2 + 12^2) = 15

    Then, z = sqrt(25^2 - 15^2) = 20.

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  3. i don't like MATH! MATH MATH MATH!

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