Answer:
[tex]y=4\sqrt{3}[/tex]
[tex]x=2\sqrt{21}[/tex]
Step-by-step explanation:
The diagram is shown in the attachment.
By the altitude -leg rule :
[tex]\frac{14-8}{y}=\frac{y}{8}[/tex]
This implies that:
[tex]\frac{6}{y}=\frac{y}{8}[/tex]
By cross multiplication:
[tex]y^2=6*8\\\implies y^2=16*3[/tex]
Take square root to get:
[tex]y=\sqrt{16*3}[/tex]
[tex]y=4\sqrt{3}[/tex]
Using the Pythagoras Theorem:
[tex]x^2=6^2+(\sqrt{48})^2[/tex]
[tex]x^2=36+48[/tex]
[tex]x^2=84[/tex]
[tex]x=2\sqrt{21}[/tex]
