An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of #32 # and the triangle has an area of #16 #. What are the lengths of sides A and B?

1 Answer
Tom M.
Nov 13, 2017

#sqrt257~~16.03#

Explanation:

First things first - we start off with a diagram!
enter image source here
Not the most elegant diagram in the world, but it does the job. By convention, the side opposite angle #A# is #a#, opposite angle #B# is #b# and #C# is #c#. #h# is the perpendicular bisector of AB at M - it cuts AB in half at a right angle.

Let #a=b=x#. Our job is to find #x#.

#Area_triangle=1/2bh#
#16=1/2xx32h#
#16=16h#
#h=1#

Now, we can apply Pythagoras' Theorem in one of the right-angled triangles. We have the height #h=1# and the base#=16#, so we can work out x.

#1^2+16^2=x^2#
#1+256=x^2#
#x^2=257#
#x=sqrt257~~16.03#

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