Two corners of an isosceles triangle are at #(5 ,7 )# and #(2 ,3 )#. If the triangle's area is #6 #, what are the lengths of the triangle's sides?

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Answer 1 · 2017-02-21T13:41:25

#sqrt[1201]/10,sqrt[1201]/10,5#

First, calling #p = (x,y)# the unknown corner coordinates, we have

#S = 1/2det((1,5,7),(1,2,3),(1,x,y))->1+4x-3y=12#

and also

#norm(p-(5,7))=norm(p-(2,3))->6x+8y=61#

Now solving

#{(1+4x-3y=12),(6x+8y=61):}#

we obtain

#x=271/50, y = 89/25#

Attached the triangle plot

enter image source here

The sides have the lengths

#sqrt[1201]/10,sqrt[1201]/10,5#