Question 584932
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