## lyzkhalifaa 2 years ago if an equillateral triangke has the perimeter of 66, what is the altitude? i just wanna know how to solve it, like the formula.

1. Hero

Well, if given the perimeter of an equilateral triangle, you can find the lengths of the sides by using the formula $S_{\text{Triangle}} = \frac{P}{3}$ |dw:1357829776184:dw| Afterwards, you'll have to draw the altitude which divides the base of the triangle in half. |dw:1357829954412:dw| Furthermore, you'd have to use Pythagorean Theorem to find the the length of the altitude

2. lyzkhalifaa

|dw:1357830348662:dw| so, how would i make this into a pythagoream theorom?

3. Hero

Split the bigger triangle into two smaller ones. Then just solve for one of the missing sides. The missing side is the altitude of course.

4. Hero

|dw:1357830687072:dw| a^2 + b^2 = c^2 a^2 + 11^2 = 22^2

5. lyzkhalifaa

i got a=24.6 .. is that right?

6. Hero

c = 22 is the hypotenuse, right? So either leg has to be less than that. In other words a < c

7. Hero

So there's no way that a = 24. 6

8. lyzkhalifaa

11x11=121 and 22x22=484, then i added them together and 605 and the squareroot of 605 was 24.6 :c

9. Hero

a^2 + 11^2 = 22^2 a^2 = 22^2 - 11^2 a^2 = 484 - 121

10. lyzkhalifaa

i got 11$\sqrt{3}$

11. lyzkhalifaa

with the 11 infront

12. lyzkhalifaa

thank you Hero (:

13. Hero

a^2 + 11^2 = 22^2 a^2 = 22^2 - 11^2 a^2 = 484 - 121 a^2 =121(4 - 1) a^2 = 121(3) a = sqrt(121*3) a = sqrt(11^2)sqrt(3) a = 11sqrt(3)