Question

1. in right triangle abc, altitude cd with length h is drawn to its hypotenuse. we also know ad = 12 and db = 3. what is the value of h?

Explanation:

Step1: Recall the geometric mean theorem (altitude-on-hypotenuse theorem)

In a right triangle, the altitude drawn to the hypotenuse is the geometric mean between the segments into which it divides the hypotenuse. So, \( h^2 = AD \times DB \).

Step2: Substitute the given values of AD and DB

We know \( AD = 12 \) and \( DB = 3 \). Substituting these into the formula, we get \( h^2 = 12 \times 3 \).

Step3: Calculate the product and then find h

First, calculate \( 12 \times 3 = 36 \). Then, take the square root of both sides: \( h = \sqrt{36} \).

Step4: Simplify the square root

\( \sqrt{36} = 6 \).

Answer:

\( 6 \)