Two corners of an isosceles triangle are at #(2 ,4 )# and #(4 ,7 )#. If the triangle's area is #9 #, what are the lengths of the triangle's sides?

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Answer 1 · 2017-07-21T14:45:42

The lengths of the sides of the triangle are #3.61u, 5.30u,5.30u#

The length of the base is

#b=sqrt((4-2)^2+(7-4)^2)=sqrt(4+9)=sqrt13=3.61#

Let the altitude of the triangle be #=h#

Then

The area of the triangle is #A=1/2*b*h#

#h=2A/b=2*9/(sqrt13)=18/sqrt13=4.99#

The sides of the triangle are

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

#=sqrt(18^2/13+13/4)#

#=5.30#