Two corners of an isosceles triangle are at #(5 ,6 )# and #(4 ,8 )#. If the triangle's area is #36 #, what are the lengths of the triangle's sides?

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Answer 1 · 2017-07-09T11:07:29

The lengths of the sides are #=2.24, 32.21,32.21#

The length of the base is

#b=sqrt((4-5)^2+(8-6)^2)=sqrt(1+4)=sqrt5#

The area of the triangle is

#A=1/2*b*h=36#

So,

The altiude is #h=36*2/b=72/sqrt5#

We apply Pythagoras' theorem

The length of the side is

#l=sqrt((b/2)^2+(h)^2)#

#=sqrt((5/4+72^2/5))#

#=sqrt(1038.05)#

#=32.21#