Two corners of an isosceles triangle are at #(6 ,4 )# and #(2 ,7 )#. If the triangle's area is #36 #, what are the lengths of the triangle's sides?

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Answer 1 · 2018-06-02T08:52:07

Length of the sides are #color(blue)(5, 14.59, 14.59#

Area of triangle #A_t = (1/2) a h#

Given #(x_b, y_b ) = (6,4), (x_c,y_c) = (2,7), A_t -= 36#

#a = sqrt((6-2)^2 + (4-7)^2) = 5#

#h = (2 * A_t)/a = (2*36)/5= 14.5#

#b = c = sqrt((5/2)^2 + 14.5^2 )= 14.59#