Question

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

Answer 1

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

Answer 2

Anyone?

Answer 3

Where is everyone?

Answer 4

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

Answer 5

42.59

Answer 6

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

Answer 7

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!

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

Correct.