Posted by **Jorge** on Tuesday, February 8, 2011 at 6:14pm.

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 -
**Reiny**, Tuesday, February 8, 2011 at 6:32pm
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 -
**helper**, Tuesday, February 8, 2011 at 6:45pm
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 -
**Jorge**, Tuesday, February 8, 2011 at 6:48pm
Thanku sooo much!

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