Question

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

Answer 1

`x=(20√(3))/(3)\ cm`

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√(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√(2)\ cm`

`C.F=x\ cm`

substitute

`20^2=(x√(2))^2+x^2`

`400=2x^2+x^2`

`400=3x^2\\\\x=\sqrt{(400)/(3)}`

simplify

`x=(20)/(√(3))\ cm`

Multiply by
`(√(3))/(√(3))`

`x=(20√(3))/(3)\ cm`