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 #45 #. What are the lengths of sides A and B?

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Answer 1 · 2016-09-20T01:51:11

#9.605#

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ABC is an isosceles triangle. #=> A=B#

Area #(A_r)=1/2 xx bxxH#

where b=base and h=height.

Given #A_r=45 and C=12#

#=> A_r=45=1/2xx12xxH#; (C=base=12)

#=> H=(45xx2)/12=7.5#

#=> A= B=sqrt(7.5^2+6^2)=sqrt92.25=9.605#