Two corners of an isosceles triangle are at #(1 ,5 )# and #(6 ,7 )#. If the triangle's area is #4 #, what are the lengths of the triangle's sides?

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Answer 1 · 2018-06-02T09:22:45

Lengths of the sides are #color(indigo)(5.39, 5.59, 5.59#

Given : # (x_b,y_b) = (1,5), (x_c,y_c) = (6,7), A_t = 4, b = c = ?#

#a = sqrt((7-5)^2 + (6-1)^2) = color(indigo)(5.39#

#h = (2 * A_t) / a = (2 * 4)/5.39 = 1.48#

#b = c = sqrt((a/2)^2 + h^2) = sqrt((5.39/2)^2 + 1.48^2) = color(indigo)(5.59)#