# In an isosceles triangle LMN, LM=39cm, NL=39cm and MN = 27cm, how do you calculate the height of the triangle LMN?

Mar 15, 2017

I got $36.6 c m$

#### Explanation:

Consider the figure:

You can apply Pythagora's Theorem to the yellow triangle and write:

${39}^{2} = {13.5}^{2} + {h}^{2}$

rearranging:

$h = \sqrt{{39}^{2} - {13.5}^{2}} = 36.6 c m$

Mar 15, 2017

Assuming a base of $L M$, the height would be (approximately) $36.59$ cm

#### Explanation:

A line segment bisecting the base and perpendicular to the base and terminating at the point $N$ has a length equal to the height.

By the Pythagorean Theorem
$\textcolor{w h i t e}{\text{XXX}} h = \sqrt{{39}^{2} - {13.5}^{2}}$
using a calculator this can be evaluated as 9approximately)
$\textcolor{w h i t e}{\text{XXX}} 36.588932753$