SOLUTION: in a right triangle a line perpendicular to the hypotenuse drawn from the midpoint of one of the sides divides the hypotenuse int o segments which are 10 cm and 6cm long. find the

Algebra ->  Triangles -> SOLUTION: in a right triangle a line perpendicular to the hypotenuse drawn from the midpoint of one of the sides divides the hypotenuse int o segments which are 10 cm and 6cm long. find the       Log On


   

Question 765725: in a right triangle a line perpendicular to the hypotenuse drawn from the midpoint of one of the sides divides the hypotenuse int o segments which are 10 cm and 6cm long. find the lengths of the two sides of the triangle
Answer by reviewermath(1029) About Me  (Show Source):
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Q:
In a right triangle a line perpendicular to the hypotenuse drawn from the midpoint of one of the sides divides the hypotenuse into segments which are 10 cm and 6cm long. find the lengths of the two sides of the triangle.
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A:

By similarity of triangles:
6%2Fx = 2x%2F16
2x%5E2 = 96
x%5E2 = 48
x = 4sqrt%283%29
2x = 8sqrt%283%29
Using Pythagorean Theorem:
y%5E2 + %288sqrt%283%29%29%5E2 = 16%5E2
y%5E2 + 192 = 256
y%5E2 = 64
y = 8
The other sides of the triangle are highlight%288sqrt%283%29%29 cm and highlight%288%29 cm.