Question

Please help with maths homework Pythagorus 3D fast !!!!

Answer 1

Answer:

$x=\frac{20\sqrt{3}}{3}\ cm$

Step-by-step explanation:

step 1

Find the length side A.C

Applying the Pythagorean Theorem in the right triangle A.B.C

$A.C^2=A.B^2+A.C^2$

we have

$A.B=x\ cm\\B.C=x\ cm$

substitute

$A.C^2=x^2+x^2\\A.C^2=2x^2\\A.C=x\sqrt{2}\ cm$

step 2

Find the value of x

Applying the Pythagorean Theorem in the right triangle A.C.F

$A.F^2=A.C^2+C.F^2$

we have

$A.F=20\ cm$

$A.C=x\sqrt{2}\ cm$

$C.F=x\ cm$

substitute

$20^2=(x\sqrt{2})^2+x^2$

$400=2x^2+x^2$

$400=3x^2\\\\x=\sqrt{\frac{400}{3}}$

simplify

$x=\frac{20}{\sqrt{3}}\ cm$

Multiply by $\frac{\sqrt{3}}{\sqrt{3}}$

$x=\frac{20\sqrt{3}}{3}\ cm$