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

1 Answer
Alan P.
Jul 26, 2016

#abs(A)=abs(B)=sqrt(3^2+(64/3)^2)~~21.5434#

Explanation:

Using #abs(C)=6# as the base and #64# as the area
the height of the triangle (relative to #C#) is
#color(white)("XXX")h=64/3# (Since #"Area" = 1/2*base*h#)

Since #triangleABC# is isosceles with #abs(A)=abs(B)#
the height (relative to side #C#) bisects the length of #C# (innto two segments of #3# each).
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Using the Pythagorean Theorem
#color(white)("XXX")abs(A)=sqrt(3^2+h^2)=sqrt(3^2+(64/3)^2)#

Using a calculator or computer we can evaluate this as
#color(white)("XXX")abs(A)~~21.5434#

(and #abs(B)=abs(A)#)

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