Answer:
x = 10
Step-by-step explanation:
An equilateral triangle has 3 congruent sides.
Let each side have length s.
P = 60 cm
P = 3s
3s = 60 cm
s = 20 cm
Each side has length 20 cm.
Draw an equilateral triangle with a horizontal side on the bottom. From the top vertex, drop a vertical segment to the horizontal side. This segment is the altitude. The altitude is the perpendicular bisector of the horizontal side of the triangle. Now you have two small congruent triangles, one on each side. One angle at the horizontal side is 60 degrees. The other is 90 degrees. The top angle is 30 degrees. Half of the bottom side of the original equilateral triangle has length 10 cm. The hypotenuse is 20 cm. The altitude is the third side.
10^2 + 20^2 = altitude^2
altitude^2 = 20^2 - 10^2
altitude^2 = 400 - 100
altitude^2 = 300
altitude^2 = 100 * 3
altitude = sqrt(100) * sqrt(3)
altitude = 10sqrt(3)
altitude = x * sqrt(3)
x = 10
