In a right angled triangle what is the relation between the square of the altitude on to the hypotenuse and the product of the segments of the hypotenuse?

Correct Answer: 0

Solution

PLACEHOLDER ANSWER - the answer is a relation. If the altitude $$h$$ divides the hypotenuse into segments $$p$$ and $$q$$, the two smaller triangles are similar to each other, which gives $$\frac{h}{p} = \frac{q}{h}$$. So the square of the altitude equals the product of the segments, $$h^2 = pq$$.

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