anonymous
  • 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.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
|dw:1441158039904:dw|
anonymous
  • anonymous
now we need the third side which we can fine by pythagoras
anonymous
  • anonymous
isn't it a 30 60 90 triangle?

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anonymous
  • anonymous
yes, it is
anonymous
  • anonymous
i'm just confused how to find the lengths i wrote out an equation but it's confusing me
anonymous
  • anonymous
so the length of the long let is the length of the short leg times \(\sqrt{3}\)
anonymous
  • anonymous
|dw:1441158247268:dw|
anonymous
  • anonymous
you have \[x+2x+\sqrt{3}x=24\]
anonymous
  • anonymous
ok you are ahead of me
anonymous
  • anonymous
haha sorry
anonymous
  • anonymous
\[3x+\sqrt{3}x=24\] good
anonymous
  • anonymous
now the question is, how do you solve for \(x\) right?
anonymous
  • anonymous
yeah that's what i'm confused on
anonymous
  • anonymous
don't you multiply by one in the form of root three over root three?
anonymous
  • anonymous
suppose \(\sqrt{3}=1.7\) and you had \(3x+1.7x=24\) what would you do?
anonymous
  • anonymous
4.7x = 24, then you'd divide
anonymous
  • anonymous
right and you got \(4.7\) by taking \(3+1.7\) you do the same thing here
anonymous
  • anonymous
\[(3+\sqrt{3})x=24\] then divide
anonymous
  • anonymous
okay, how would i solve if i needed to keep everything in simple radical form ?
anonymous
  • anonymous
does it say round?
anonymous
  • anonymous
it does but usually the teacher wants it in the other form
anonymous
  • anonymous
http://www.wolframalpha.com/input/?i=24%2F%283%2Bsqrt%283%29%29
anonymous
  • anonymous
you can rationalize the denominator if you like
anonymous
  • anonymous
okay, i think i get it. thank you
anonymous
  • anonymous
yw

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