1. ## Special right triangles

I'm really confused with a word problem trying to find the sides of a triangle with just an altitude or a perimeter.

How would I found the length of a side of an equilateral triangle with an altitude of 24? I know altitude divides the triangle in half, so would it be a 45-45-90 triangle?

Also how would I find the altitude of an equilateral triangle with a perimeter of 45?

2. Originally Posted by Jubbly
I'm really confused with a word problem trying to find the sides of a triangle with just an altitude or a perimeter.

How would I found the length of a side of an equilateral triangle with an altitude of 24? I know altitude divides the triangle in half, so would it be a 45-45-90 triangle?

Also how would I find the altitude of an equilateral triangle with a perimeter of 45?

Hi Jubbly,

Actually, the altitude will divide the equilateral triangle into two 30-60-90 congruent right triangles.

You know in a 30-60-90 configuration, the altitude is equal to the short side (x) times the square root of 3.

$\displaystyle 24=x\sqrt{3}$

$\displaystyle x=\frac{24}{\sqrt{3}}=8\sqrt{3}$

The hypotenue is the length of the side of the equilateral triangle and is two times the short side.

Thus, the side of the equilateral triangle is $\displaystyle 16\sqrt{3}$

If the perimeter of an equilateral triangle is 45, then each side would be 15. This would mean that in your triangular configuration, 15 is the hypotenuse. The short side would be 7.5 (half the hypotenue) and the long side (altitude) would be $\displaystyle 7.5\sqrt{3}$