Question

Find the value of x and y. Write the answers in simplest radical formx= y=

Answer 1

Let's redraw the traingle

if the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other. ∆CBD ~ ∆ABC, ∆ACD ~ ∆ABC, and ∆CBD ~ ∆ACD.

This means that

`\begin{gathered} (BD)/(CD)=(CD)/(AD) \\ \\ (AB)/(CB)=(CB)/(DB) \end{gathered}`

Replacing

`\begin{gathered} (3)/(x)=(x)/(9) \\ \\ x^2=27 \\ x=√(27)=3√(3) \end{gathered}`
`\begin{gathered} (12)/(y)=(y)/(3) \\ \\ y^2=36 \\ y=√(36)=6 \end{gathered}`