In a right triangle ABC, the altitude is drawn from 90 degree angle A to a point P on the hypotenuse. This altitude is 6 cm and the length of the hypotenuse is 20 cm.

What are the measures of the two segments BP and CP on the hypotenuse? Any help would be great. Thank you

Guest Nov 14, 2018

#1**+1 **

Let BP = x and CP = 20 - x

In this situation, the altitude will be a "geometric mean"....such that

x 6

__ = _____

6 20 - x

Cross-multiply

x (20 - x) = 36

20x - x^2 = 36 rearrange as

x^2 - 20x + 36 = 0 factor

(x - 2) ( x - 18) = 0

Set each factor to 0 and solve for x and we get that x = 2 or x = 18

So.....depending upon which vertex is labeled as B and which is labeled C.....

BP = 2 and CP = 18 or

BP = 18 and CP = 2

Either way.....the hypotenuse is divided into a ratio of 18 : 2

CPhill Nov 14, 2018