Question

3potniIn a right triangle, the altitude drawn to the hypotenuse divides the hypotenuse into two segments of equal lengths 8 cm and 2 cm. What is the length of the altitude?O 10 cm

Answer 1

`\text{The altitude is 4cm.}`

Explanation:

Let's illustrate the situation in a diagram to understand.

In a right triangle if the altitude drawn divides the hypotenuse into two segments, then the length of the altitude is the geometric mean of the lengths of the two segments.

Therefore,

`\begin{gathered} (8)/(a)=(a)/(2) \\ 2\cdot8=a^2 \\ 16=a^2 \\ a=\sqrt[]{16} \\ a=4\text{ cm} \end{gathered}`