If BC = 7 and CD = 24, find AC.

Question

Vocaloid · Answer

Is there a diagram associated w/ this question?

Angle · Answer

|dw:1529330039415:dw|

Angle · Answer

Here are the lengths that are given
|dw:1529330501074:dw|

Logic007 · Answer

I think we will need to make two eqns using pythagoras theorem

Angle · Answer

All the right triangles involved are similar triangles. We can use this and proportions to get to the answer.

Logic007 · Answer

Oh yeah,another way to solve it.
*Thumbs up*

Logic007 · Answer

My brain is malfunctioning >.<
can u show me how u do that proportion? @Angle

Angle · Answer

Yeah, sorry, my drawing tool wasn't working properly
|dw:1529331158397:dw|
|dw:1529331257769:dw|

Angle · Answer

so we can set up the proportional fractions:
$\large \frac{x}{24} = \frac{7}{x}$
*note there are other ways to represent this proportion

Logic007 · Answer

$AD^2=AC^2+24^2$
$AD^2=31^2-AB^2$
$31^2-AB^2=AC^2+24^2$
$AB^2=AC^2+7^2$
$31^2-(AC^2+7^2)=AC^2+24^2$
$31^2-24^2=AC^2+7^2+AC^2$
$2AC^2=31^2-24^2-7^2$
$2AC^2=336$
$AC^2=168$
$AC=\sqrt{168}$

Logic007 · Answer

Cool,we got the same answer :D
Thanks for showing me that working

Angle · Answer

yup ^_^
plus, I think the square root can be simplified a little more
but it's great to have more than one way to solve something :)

Logic007 · Answer

Haha,true ;)
But I think your working for this question is much better bcoz it is simple,lol :D