數學問題－求邊長

設 x = 三角形邊長,
面積 = 0.5*底*高 = 4√3
= 0.5x*高 = 4√3
高 = 8√3/ x

三角形邊長關係, 畢氏定理,
(高)^2 + (1/2 x)^2 = x^2
(8√3/x)^2 + (1/2 x)^2 = x^2
192/x^2 + x^2/4 = x^2
(192/x^2 + x^2/4)*4x^2 = x^2*4x^2 (全條式乘 4x^2)
192*4 + x^4 = 4x^4
768 = 3x^4
x^4 = 256
x = 4 (-4 rejected)
三角形邊長 4 厘米

Let x=length of the side; h=height of the triangle

SInce the length of sides are equal, the angle must be 60°

sin 60° = h/x
(root 3)/2 = h/x
so h = x (root 3) / 2

Area = h.x/2 = (x^2) (root 3) / 4

(x^2) (root 3)/4 = 4(root 3)
x^2 = 16
x=4 (length of each side)