Question 1114382: the altitude drawn to the hypotenuse of a right triangle divides the hypotenuse so that
a) h is the geometric mean of x and y,
b) a is the geometric mean of x and c, and
c) b is the geometric mean of y and c
Use this theorem to calculate lengths h, a, and b if x=144 and y = 25.
solve using geometric sequence
Answer by greenestamps(13215)   (Show Source):
You can put this solution on YOUR website!
Although you don't define the variables, it seems obvious from the statement of the problem that x and y are the two segments of the hypotenuse c, and h is the altitude to side c.
x = 144 = 12^2; y = 25 = 5^2; so h is 12*5 = 60.
So the original triangle and both of the small triangles formed by the altitude are scale models of a 5-12-13 right triangle.
That makes a and b 65 and 156; from the given description of the problem, we don't know which is which....
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