Question

the altitude to the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 5 and 15. what is the length of the altitude? a. 3 b. $5sqrt{3}$ c. 10 d. $5sqrt{5}$

Explanation:

Step1: Recall geometric mean theorem

For a right triangle, the altitude $h$ to the hypotenuse satisfies $h^2 = p \times q$, where $p$ and $q$ are the lengths of the hypotenuse segments.

Step2: Substitute given values

$p=5$, $q=15$, so $h^2 = 5 \times 15$

Step3: Calculate and solve for $h$

$h^2=75$, so $h=\sqrt{75}=\sqrt{25 \times 3}=5\sqrt{3}$

Answer:

B. $5\sqrt{3}$