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Each side of an equilateral triangle measures 12 cm. Find the height, h, of the triangle

1 Answer

2 votes

Answer:

_

ℎ = 6v5

Explanation:

To find the height (

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:

2

=

2

+

2

h

2

=a

2

+s

2

2

=

6

2

+

1

2

2

h

2

=6

2

+12

2

2

=

36

+

144

h

2

=36+144

2

=

180

h

2

=180

=

180

=

6

5

cm

h=

180

=6

5

cm

So, the height

h of the equilateral triangle is

6

5

cm

6

5

cm.

User Sprockets
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