Question

Find the value of each variable. Write your answer in simplest radical form.

Answer 1

Answer:

$y=4\sqrt{3}$

$x=2\sqrt{21}$

Step-by-step explanation:

The diagram is shown in the attachment.

By the altitude -leg rule :

$\frac{14-8}{y}=\frac{y}{8}$

This implies that:

$\frac{6}{y}=\frac{y}{8}$

By cross multiplication:

$y^2=6*8\\\implies y^2=16*3$

Take square root to get:

$y=\sqrt{16*3}$

$y=4\sqrt{3}$

Using the Pythagoras Theorem:

$x^2=6^2+(\sqrt{48})^2$

$x^2=36+48$

$x^2=84$

$x=2\sqrt{21}$