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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 #18 # and the triangle has an area of #72 #. What are the lengths of sides A and B?

1 Answer

Feb 8, 2017

#sqrt145~~12.04#

Explanation:

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Given : #A=B, C=18#, and Area#=72#

As Area #=1/2*b*h#,
where #b# is the base and #h# is the height.
Here, #b=C=18#
#=> 72=1/2*18*h#
#=> h=8#

By Pythagorean theorem, we know that
#A^2=h^2+(C/2)^2#
#=> A=sqrt(8^2+(18/2)^2)=sqrt145#

Hence, #A=B=sqrt145~~12.04# units

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