SOLUTION: Find the area of right triangle , given that the altitude to the hypotenuse separates the hypotenuse into segments of lenghts 44 cm and 11 cm .

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Question 700477: Find the area of right triangle , given that the altitude to the hypotenuse separates the hypotenuse into segments of lenghts 44 cm and 11 cm .
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
h=sqrt%2811%2A44%29 (The length of that green altitude is the geometric mean of the two segments).
They are supposed to teach you that in geometry, but it is easy to prove,
because the original triangle,
and the two triangles to either side of the altitude,
are similar right triangles (congruent angles, proportional sides).
So the ratio of long leg to short leg in the small triangle is the same:
h%2F11=44-h --> h%5E2=11%2A44 --> h=sqrt%2811%2A44%29

So to calculate the area of the large triangle, we take the hypotenuse as the base, b of the triangle:
b=44%2B11 cm --> highlight%28b=55%29 cm
The height, h, is the length of that altitude:
h=sqrt%2811%2A44%29 --> h=sqrt%2811%2A11%2A4%29 --> h=sqrt%2811%2A11%29%2Asqrt%284%29 --> h=11%2A2 --> highlight%28h=22%29 cm

For a triangle, area=b%2Ah%2F2.
In this case area=55%2A22%2F2 --> highlight%28area=605%29 cm%5E2