Question

What's the length of the |AC| ?

Answer 1

`AC=5sqrt2`

Explanation:

If `AB ⊥ BC`, and `AB=5`, then `BC=5`. This is a right angled triangle, which means sides`a^2+b^2=c^2`. In this case `a=AB=5,` `b=BC=5,` and `c=AC`. Therefor
`5^2+5^2=(AC)^2`
`25+25=(AC)^2`
`50=(AC)^2`
`sqrt50=AC`

From here we can simplify `sqrt50`, since
`sqrt50=sqrt(5*5*2)=5sqrt2`

I hope I helped!

Answer 2

`AC=8 1/3cm.`

Explanation:

As `BH=3` and `AB=5`, as `Delta ABH` is right angled at `H`, using Pythagoras Theorem

`AH=sqrt(5^2-3^2)=sqrt(25-9)=sqrt16=4`

In a right angled triangle, right angled at `/_B`, if we connect midpoint of hypotenuse to `B`, then

`BD=AD=DC`.

Ler this be `x` and then `HD=x-3` and using Pythagoras Theorem on `DeltaAHD`, we have

`AH^2+HD^2=AD^2` or `4^2+(x-3)^2=x^2`

i.e. `x^2-6x+9+16=x^2`

or `6x=25` and `x=25/6=4 1/6`

Hence, `AC=25/6xx2=25/3=8 1/3cm.`