SOLUTION: the altitude of a right triangle divides the hypotenuse into two segments of 8cm and 2cm length. Find the area of triangle

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Question 1172201: the altitude of a right triangle divides the hypotenuse into two segments of 8cm and 2cm length. Find the area of triangle
Found 2 solutions by Boreal, mccravyedwin:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Draw this.
Similar triangles with the altitude x
2/x=x/8, the geometric mean, is the sqrt (2*8), or 4 cm
the base is the hypotenuse of 10 cm
The area is 1/2 bh=20 cm^2

Answer by mccravyedwin(408) About Me  (Show Source):
You can put this solution on YOUR website!
Oh darn, he did it for you before I could post this!
----------------------------------------------------------
Instead of doing your problem for you, I'll do one that is exactly like
yours in every way, step by step.  

The problem I will do is this one:

the altitude of a right triangle divides the hypotenuse into two segments of 9cm and 4cm length. Find the area of triangle

Sketch the triangle:



Find the length of the altitude:



matrix%281%2C3%2C9%2Fh%2C%22%22=%22%22%2Ch%2F4%29

Cross multiply:

matrix%281%2C3%2Ch%2Ah%2C%22%22=%22%22%2C9%2A4%29

matrix%281%2C3%2Ch%5E2%2C%22%22=%22%22%2C36%29

matrix%281%2C3%2Ch%2C%22%22=%22%22%2Csqrt%2836%29%29

matrix%281%2C3%2Ch%2C%22%22=%22%22%2C6%29

matrix%281%2C3%2CArea%2C%22%22=%22%22%2Cbase%2Aaltitude%29

matrix%281%2C3%2Cbase%2C%22%22=%22%22%2C9%2B4%29

matrix%281%2C3%2Cbase%2C%22%22=%22%22%2C13%29

matrix%281%2C3%2Caltitude%2C%22%22=%22%22%2Ch%29

matrix%281%2C3%2Ch%2Ah%2C%22%22=%22%22%2C6%29

matrix%281%2C3%2Ch%2Ah%2C%22%22=%22%22%2C9%2A4%29

matrix%281%2C3%2CArea%2C%22%22=%22%22%2Cbase%2Aaltitude%29

matrix%281%2C3%2CArea%2C%22%22=%22%22%2C13%2A6%29

matrix%281%2C4%2CArea%2C%22%22=%22%22%2C78%2Ccm%5E2%29

Now do your problem exactly the same way, step by step.

Edwin