the area of an equilateral triangle is 100v3 sqare inches. how long are its sides

Question

can some one please help me solve this

Answer 1

The area of an equilateral triangle of side s = s²√3 /4

 

s²√3 /4 = 100 √3

 

solve for s.

 

Answer 2

First, let me say that I really wish I could draw a picture. I'll do my best to describe it in words, so if you can draw it as I explain it, hopefully that'll help.

 

You know that the area of a triangle is A = 1/2bh. Since an equilateral triangle has 3 equal sides and 3 equal angles (60 degrees), the b will be what you're solving for. You were given A, and the h would be the distance from one vertex to the middle of the opposite side. (Picture an equilateral triangle with one point at the top and a flat bottom. Now draw the line straight down connecting that point to the middle of the bottom. You now have 2 triangles whose angles are 30-60-90.)

Now, since these smaller triangles are 30-60-90 triangles, you know the ratio of their sides is b/2, b, and b√3/2. Thus, your h = b√3/2. (If you're wondering where that came from, the ratio is always 1:2:√3. Since the middle length side is b, the smaller side has to be b/2, and the longest side (hypotenuse) is the shortest side times square root 3.)

Therefore, A = 1/2bh is now
100v3 sq in = 1/2·b·b√3/2
and you can use algebra to solve for b, and don't forget your units!

Again, I'm sorry I don't know how to use pictures in the questions area here. I hope this was at least somewhat helpful.