Question

In right triangle ABC, altitude CD withlength h is drawn to its hypotenuse. Wealso know AD 12 and DB = 3. What isthe value of h?

Answer 1

`\begin{gathered} \text{Taking triangle DCB, we have:} \\ x^2=h^2+3^2 \\ x^2=h^2+9\ldots eqn\text{ a)} \end{gathered}`
`\begin{gathered} \text{Taking triangle ACD, we have:} \\ y^2=h^2+12^2 \\ y^2=h^2+144\ldots eqn\text{ b)} \end{gathered}`
`\begin{gathered} \text{Taking triangle ACB, we have:} \\ 15^2=x^2+y^2 \\ Substituting\text{ the equations a) and b) above, we have:} \\ 15^2=h^2+9+h^2+144 \\ 225-9-144=2h^2 \\ 2h^2=72 \\ h^2=(72)/(2) \\ h^2=36 \\ h=\sqrt[]{36} \\ h=6 \end{gathered}`

Hence, the value of height,h, is 6