SOLUTION: One equilateral triangle has sides 5 ft long. Another equilateral triangle has sides 7 ft long. Find the ratio of the areas of the triangles. I think I need to start with the simil

Algebra ->  Triangles -> SOLUTION: One equilateral triangle has sides 5 ft long. Another equilateral triangle has sides 7 ft long. Find the ratio of the areas of the triangles. I think I need to start with the simil      Log On


   

Question 584932: One equilateral triangle has sides 5 ft long. Another equilateral triangle has sides 7 ft long. Find the ratio of the areas of the triangles. I think I need to start with the similarity ratio. But I'm not sure, and I don't know where to go from there! Thank you. (:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If the side length of an equilateral triangle is x units, then the height/altitude is (x/2)*sqrt(3) units.

So the area is then A = (bh)/2 = (x*(x/2)*sqrt(3))/2 = ((x^2)/4)*sqrt(3)


So in short, the area of the equilateral triangle with side length 'x' is ((x^2)/4)*sqrt(3) square units.


So the triangle with sides 5 ft long has an area of ((5^2)/4)*sqrt(3) = (25/4)*sqrt(3)


and the triangle with sides 7 feet long has an area of ((7^2)/4)*sqrt(3) = (49/4)*sqrt(3)


Divide the two to get ( (25/4)*sqrt(3) )/( (49/4)*sqrt(3) ) = (25/4)(4/49) = 25/49


So the ratio between the two areas is 25:49