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 #4 # and the triangle has an area of #36 #. What are the lengths of sides A and B?

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Answer 1 · 2016-05-30T14:35:35

The equal sides of the triangle are #sqrt(328)=2sqrt(82)~~18.1# units long

Using the information about triangle's area we have:

#A=36#

#1/2*4*h=36#

#2h=36#

#h=18#

Now we can calculate the remaining side using Pythagorean Theorem:

#2^2+18^2=b^2#

#4+324=b^2#

#b^2=328#

#b=sqrt(328)=2sqrt(82)~~18.1#