## anonymous one year ago 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.

1. anonymous

|dw:1441158039904:dw|

2. anonymous

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

3. anonymous

isn't it a 30 60 90 triangle?

4. anonymous

yes, it is

5. anonymous

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

6. anonymous

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

7. anonymous

|dw:1441158247268:dw|

8. anonymous

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

9. anonymous

ok you are ahead of me

10. anonymous

haha sorry

11. anonymous

$3x+\sqrt{3}x=24$ good

12. anonymous

now the question is, how do you solve for $$x$$ right?

13. anonymous

yeah that's what i'm confused on

14. anonymous

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

15. anonymous

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

16. anonymous

4.7x = 24, then you'd divide

17. anonymous

right and you got $$4.7$$ by taking $$3+1.7$$ you do the same thing here

18. anonymous

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

19. anonymous

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

20. anonymous

does it say round?

21. anonymous

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

22. anonymous
23. anonymous

you can rationalize the denominator if you like

24. anonymous

okay, i think i get it. thank you

25. anonymous

yw