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 #16 # and the triangle has an area of #64 #. What are the lengths of sides A and B?

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Answer 1 · 2016-10-08T02:17:43

#8sqrt2=11.3137#

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Given #A=B, C=16#, Area #A_r=64#,

#=> A_r=1/2*C*h#
#=> 64=1/2*16*h, => h=8#

#A^2=h^2+(C/2)^2#

#=> A^2=8^2+(16/2)^2=8^2+8^2=128#

#=> A=sqrt128=sqrt(64*2)=8sqrt2=11.3137#

Hence, #A=B=11.3137#