SOLUTION: In a right angle triangle, a line perpendicular to the hypotenuse drawn from the midpoint of one of the sides divides the hyootenuse into segment which are 10 cm and 6 cm long. Fin

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Question 979057: In a right angle triangle, a line perpendicular to the hypotenuse drawn from the midpoint of one of the sides divides the hyootenuse into segment which are 10 cm and 6 cm long. Find the lengths of the two sides of the triangle.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
In a right triangle, the altitude to the hypotenuse splits the triangle into two smaller right triangles, and you end up with three similar right triangles
As a consequence, there is a bunch of proportions between the lengths of the sides of those triangles that are useful to solve this problem.
You may even have had to memorize some formulas/theorems based on that.
b%2Fa=d%2Fb<--->b%5E2=ad , and c%2Fa=e%2Fc<--->c%5E2=ae .
In this problem there is another perpendicular to the hypotenuse, like this

That perpendicular is splitting in half the hypotenuse and one leg of one of the smaller triangles.
In the problem a=10cm%2B6cm=16cm ,
and it must be that e%2F2=6cm<-->e=2%2A6cm=12cm ,
because e%2F2=10cm-->e=20cm%3E16cm=a does not make sense.
Since e=12cm , then d=a-e=16cm%2B12cm=4cm
Using the proportions above,
b%5E2=ad-->b=sqrt%28ad%29=sqrt%28%2816cm%29%284cm%29%29=sqrt%2864cm%5E2%29=highlight%288cm%29 and
c%5E2=ae-->