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The altitude upon the hypotenuse of a right triangle divides the hypotnuse into segments of 3 and 12. find the length of the altitude

  • geometry -

    let that altitude be x

    Can you see how that altitude splits your right-angled triangle into two smaller right-angled triangles which are similar?
    so you can set up the ratio
    12/x= x/3
    x^2= 36
    x = 6

  • geometry -

    The measure of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse.

    Triangle ABC, where A is the vertex, CB is the hypotenuse, and AD is the altitude.

    AD = altitude, CD = 3, DB = 12
    AD/DB = CD/AD
    AD/12 = 3/AD
    (AD)^2 = 36
    AD = (sqrt(3 * 12))
    AD = (sqrt(36))
    AD = 6

  • geometry -

    Thanku sooo much!

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