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

2 Answers
Gió
Mar 15, 2017

I got #36.6cm#

Explanation:

Consider the figure:
enter image source here
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#

Alan P.
Mar 15, 2017

Assuming a base of #LM#, the height would be (approximately) #36.59# cm

Explanation:

enter image source here

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#

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