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# Geometry help.

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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

Nov 14, 2018

### 2+0 Answers

#1
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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

Nov 14, 2018
edited by CPhill  Nov 14, 2018
#2
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CPhill: Thank you so much, Sir.

Nov 14, 2018