43.3 = hb/2, draw the triangle with the height (h) shown. It will be one leg of a 30/60 right triangle having a base of b/2. Using the known side proportions of that triangle as 1:2:(3^1/2) ; h = (3*1/2) b/2
Therefore 43.3 = (3^1/2) (b^2) /4 so b^2 = 4(43.3) / 3^1/2 = 100 and b =10
so h= (3^1/2) 10/ 2 and height = 17.32 / 2 = 8.66 Answer
Check : 8.66 * 10 /2 = 43.3
Area of a triangle = ? base × height
Equilateral height = √3/2× side
Equilateral Area = (√3)/4×base2
43.3 = √(3)/4×b2
b = √(43.3×4)/√3) = 10
Height = √3/2×10
Let L be the length of each side, and with a equilateral triangle the angles are 60o.
Height = L*sin(60o)
Area = 43.3 = 1/2 * L * L*sin(60o).
I leave you with the rest to finish
1. A = bh / 2; where b = base which is also equal to any side, h = height
h = b*sin(60) = b*sqrt(3) / 2
b = h / (sqrt(3) / 2)
b = 2h / sqrt(3); substitute 2h / sqrt(3) for b in first equation.
A = h*(2h / sqrt(3)) / 2
43.3 = 2h^2 / (2*sqrt(3))
43.3 = h^2 / sqrt(3)
h^2 = 43.3*sqrt(3) = 75
h = 8.66
To check this answer: 8.66 = b*sin(60); where b is length of any side.
b = 8.66 / sin(60) = 10.0
A = bh / 2 = 8.66 * 10 / 2 = 43.3 check!
Area = base x 1/2 height, so twice area = base x height. Then both will be equal.
Sqrt. (43.3 x 2) = 9.3059 whatever units they are.
Not sure what to do :(
