# The perimeter of an equilateral triangle is 32 centimeters. How do you find the length of an altitude of the triangle?

##### 2 Answers

#### Answer:

Calculated "from grass roots up"

#### Explanation:

Using Pythagoras

So we need to find

We are given that the perimeter is 32 cm

So

So

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Substituting these value into equation (1) gives

There is a very well known algebra method hear where if we have

also

By looking at the 'factor tree' we have

giving:

#### Answer:

Calculated using a quicker method: By ratio

#### Explanation:

If you had an equilateral triangle of side length 2 then you would have the condition in the above diagram.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We know that the perimeter in the question is 32 cm. So each side is of length:

So

So by ratio, using the values in this diagram to those in my other solution we have:

so