An equilateral triangle has side length 6. If a horizontal line is placed in the figure such that the triangle is split into two sections of equal area, how high must the line be?
1 Answer
Dec 11, 2015
1.52 in
Explanation:
An equilateral triangle has 60 degree angles.
The height of the triangle is sin 60 x 6 inches = 5.196 inches.
So the area of the triangle is 1/2 x 6 in x 5.196 in = 15.588 sq in
and the half area is 7.494 sq in.
The base of any equilateral triangle is 1.155 times its height (see 6 in / 5.196 in) so base = 1.155h
A = 7.494 sq in = 1/2 b*h = 1/2 (1.155h) * h =0.5775 h^2
7.494 sq in = 0.5775 h^2
h^2 = 7.494/.5775= 12.9766 sq in
h = 3.674in
This is the height of the top triangle, so it is subtracted from the original height
5.196 in - 3.674 in = 1.52 in.
