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?

1 Answer
Feb 21, 2017

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

Explanation:

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