Answer:
x = 10
Step-by-step explanation:
Look at the picture.
Use the Pythagorean theorem to calculate y:
[tex]y^2+8^2=12^2[/tex]
[tex]y^2+64=144[/tex] subtract 64 from both sides
[tex]y^2=80\to y=\sqrt{80}[/tex]
Two smaller triangles are similar. Therefore the sides are in proportion:
[tex]\dfrac{x}{y}=\dfrac{y}{8}[/tex] cross multiply
[tex]y^2=8x[/tex] substitute y² = 80
[tex]80=8x[/tex] divide both sides by 8
[tex]x=10[/tex]
