Question

When an altitude is drawn to the hypotenuse of a right triangle, the lengths of the segments of the hypotenuse are 16 and 25. What is the length of the altitude?

20
25
41
50

Answer 1

We can consider these two triangles as similar triangles and how the ratios of the sides are equal:
\[ \frac{a}{16} = \frac{25}{a} \]
Here, we just have to solve for the positive a.

Answer 2

So I crossed multiplied and got 2a = 400. That would then equal 200. But that doesn't seems right?

Answer 3

Well, you're right to cross multiply. However, the problem is that:
a*a =/= 2a
2a = a + a.
a^2 = a*a (a to the power of 2)

Answer 4

So, rather than "2a = 400," we have "a^2 = 400"
and then we take the positive square root. of both sides to cancel the exponent. :)

Answer 5

So the answer is 20?

Answer 6

Yes. :)