Question

In triangle △JKL, ∠JKL is right angle, and KM is an altitude. JL=25 and JM=5, find KM.

HELP ME PLEASE!!!!!!

Answer 1

KM = 15

Explanation:

From the diagram, ΔJKL and ΔJKM are similar to each other because they share the same angle J and they are both right angle triangle. Therefore they are similar by AA property.

Since JL=25 and JM=5, JM = JL + JM= 25 + 5 = 30

Since ΔJKL and ΔJKM are similar to each other, therefore:

`(JK)/(JL)=(JM)/(JK)\\ Substituting:\\(JK)/(30)=(5)/(JK)\\JK^2=150\\JK=√(150)\\ \\From\ hypotenuse:\\JK^2=JM^2+KM^2\\Substituting:\\(√(150) )^2=5^2+KM^2\\150=25+KM^2\\KM^2=150-25=125\\KM=√(125)\\ KM=15`