Question

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

Answer 1

I got `36.6cm`

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)=36.6cm`

Answer 2

Assuming a base of `LM`, 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
`color(white)("XXX")h=sqrt(39^2-13.5^2)`
using a calculator this can be evaluated as 9approximately)
`color(white)("XXX")36.588932753`