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

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Answer 1 · 2016-06-20T08:43:29

Sides #A# and #B# have length of #sqrt(260)=2sqrt(65)#

From the given area #A=112# we can calculate the heigth:

#A=1/2*a*h#

#1/2*16*h=112#

#8h=112#

#h=14#

Now we can use the Pythagorean theorem to calculate the length of the equal sides:

#8^2+14^2=b^2#

#b^2=64+196#

#b^2=260#

#b=2sqrt(65)#