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 #12 # and the triangle has an area of #81 #. What are the lengths of sides A and B?

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Answer 1 · 2016-03-24T22:32:51

I found #14.77#

Consider the diagram:
enter image source here
The Area is given as:

#"Area"=("Base"xx"Height")/2(CxxH)/2=81#

So:

#(12*H)/2=81#
#H=81/6=13.5#

We use half triangle and Pythagoras:

#A^2=H^2+(C/2)^2=H^2+C^2/4=13.5^2+12^2/4=182.25+36=218.25#

and:

#A=sqrt(218.25)=14.77=B#