Question

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

Answer 1

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

Answer 2

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

Answer 3

Thanku sooo much!