Answer:
_
ℎ = 6v5
Explanation:
To find the height (
ℎ
h) of an equilateral triangle with side length
12
cm
12 cm, we can use the Pythagorean theorem. When you draw a line from one of the vertices to the midpoint of the opposite side, it bisects the equilateral triangle into two right-angled triangles.
Let's label one side of the triangle as
�
a, where
�
a is half of the equilateral triangle's side:
�
=
1
2
×
12
=
6
cm
a=
2
1
×12=6 cm
Now, applying the Pythagorean theorem:
ℎ
2
=
�
2
+
�
2
h
2
=a
2
+s
2
ℎ
2
=
6
2
+
1
2
2
h
2
=6
2
+12
2
ℎ
2
=
36
+
144
h
2
=36+144
ℎ
2
=
180
h
2
=180
ℎ
=
180
=
6
5
cm
h=
180
=6
5
cm
So, the height
ℎ
h of the equilateral triangle is
6
5
cm
6
5
cm.