Two corners of an isosceles triangle are at #(9 ,6 )# and #(4 ,2 )#. If the triangle's area is #64 #, what are the lengths of the triangle's sides?

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Answer 1 · 2018-06-02T08:42:02

Lengths of the sides are #color (crimson)(6.41,20.26,20.26#

Let the sides be a, b, c with b = c.

#a = sqrt((9-4)^2 + (6-2)^2) = 6.41#

#h = (2 * A_t) / a = (2*64)/sqrt(41) = 20#

#b = c = sqrt((a/2)^2 + h^2) = sqrt((6.41/2)^2 + 20^2) = 20.26#

Lengths of the sides are #color (crimson)(6.41,20.26,20.26#