## anonymous one year ago Challenge! Ready? the length of the hypotenuse of a 30 degrees-60 degrees-90 degrees triangle is 18. What is the perimeter?

1. anonymous

haha lol ok im gone!!!!!!!

2. anonymous

Anyone?

3. anonymous

Where is everyone?

4. anonymous

Finally, some people. I have to wait at least a half an hour to fluttering get an answer.

5. anonymous

42.59

6. anonymous

Whoops, should put work too. Are you doing this as a challenge?

7. AakashSudhakar

If it's a 30-60-90 triangle, that means that the appropriated ratios of the lengths of triangle sides, opposite from the 30 degree angle, 60 degree angle, and 90 degree angle, are x, x*sqrt(2), and 2x, respectively. You have the value of the hypotenuse, which corresponds to the side opposite of the 90 degree angle, which is 2x. You can quickly solve for x, getting 9. Then, summing all the sides gets you the perimeter formula, which is: $Perimeter = x + x \sqrt 2+2x$ Knowing that x = 9, simply plug in for X and solve the equation to get the perimeter of the triangle!

8. anonymous

$\large \sf 18 (H)~+~\frac{1}{2}18(SL)~+~\frac{1}{2}18 \sqrt{3}(LL)$

9. AakashSudhakar

My apologies, @LegendarySadist had it correct that I had incorrect. The aforementioned side X*sqrt(2) should be X*sqrt(3).

10. anonymous

It would be $\large \sf Perimeter~=~x+x\sqrt{3}+2x$

11. anonymous

Correct.