The altitude of an equilateral triangle is 12cm. Find the length of the sides.
You know the angles of an equilateral triangle are 60º each.
The altitude will form a right-angles triangle with angles 30,60,90º
the lengths of those sides could be 1,√3, and 2
so by ratios:
x/2 = 12/√3
x = 24/√3 = 13.856
or
sin 60 = 12/x
x = 12/sin60 = 13.856
To find the length of the sides of an equilateral triangle, you can use the formula:
s = h * sqrt(3) / 2
where s represents the length of each side and h represents the altitude.
In this case, the altitude is given as 12 cm. Therefore, the formula becomes:
s = 12 cm * sqrt(3) / 2
To find the length of the sides, we need to evaluate this expression. Let me calculate it for you.
s = 12 cm * sqrt(3) / 2
s = (12 cm * 1.732) / 2
s = 20.784 cm
Therefore, the length of each side of the equilateral triangle is approximately 20.784 cm.