Answer:
[tex]x=\frac{20\sqrt{3}}{3}\ cm[/tex]
Step-by-step explanation:
step 1
Find the length side A.C
Applying the Pythagorean Theorem in the right triangle A.B.C
[tex]A.C^2=A.B^2+A.C^2[/tex]
we have
[tex]A.B=x\ cm\\B.C=x\ cm[/tex]
substitute
[tex]A.C^2=x^2+x^2\\A.C^2=2x^2\\A.C=x\sqrt{2}\ cm[/tex]
step 2
Find the value of x
Applying the Pythagorean Theorem in the right triangle A.C.F
[tex]A.F^2=A.C^2+C.F^2[/tex]
we have
[tex]A.F=20\ cm[/tex]
[tex]A.C=x\sqrt{2}\ cm[/tex]
[tex]C.F=x\ cm[/tex]
substitute
[tex]20^2=(x\sqrt{2})^2+x^2[/tex]
[tex]400=2x^2+x^2[/tex]
[tex]400=3x^2\\\\x=\sqrt{\frac{400}{3}}[/tex]
simplify
[tex]x=\frac{20}{\sqrt{3}}\ cm[/tex]
Multiply by [tex]\frac{\sqrt{3}}{\sqrt{3}}[/tex]
[tex]x=\frac{20\sqrt{3}}{3}\ cm[/tex]
