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- anonymous

A right triangle has a 24-cm perimeter, and its hypotenuse is twice as long as it's shortest leg. To the nearest tenth of an inch. find the length of all three sides.

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- anonymous

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- anonymous

|dw:1441158039904:dw|

- anonymous

now we need the third side which we can fine by pythagoras

- anonymous

isn't it a 30 60 90 triangle?

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- anonymous

yes, it is

- anonymous

i'm just confused how to find the lengths
i wrote out an equation but it's confusing me

- anonymous

so the length of the long let is the length of the short leg times \(\sqrt{3}\)

- anonymous

|dw:1441158247268:dw|

- anonymous

you have \[x+2x+\sqrt{3}x=24\]

- anonymous

ok you are ahead of me

- anonymous

haha sorry

- anonymous

\[3x+\sqrt{3}x=24\] good

- anonymous

now the question is, how do you solve for \(x\) right?

- anonymous

yeah that's what i'm confused on

- anonymous

don't you multiply by one in the form of root three over root three?

- anonymous

suppose \(\sqrt{3}=1.7\) and you had \(3x+1.7x=24\) what would you do?

- anonymous

4.7x = 24, then you'd divide

- anonymous

right and you got \(4.7\) by taking \(3+1.7\)
you do the same thing here

- anonymous

\[(3+\sqrt{3})x=24\]
then divide

- anonymous

okay, how would i solve if i needed to keep everything in simple radical form ?

- anonymous

does it say round?

- anonymous

it does but usually the teacher wants it in the other form

- anonymous

http://www.wolframalpha.com/input/?i=24%2F%283%2Bsqrt%283%29%29

- anonymous

you can rationalize the denominator if you like

- anonymous

okay, i think i get it. thank you

- anonymous

yw

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