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
+128460 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
