Two corners of an isosceles triangle are at #(7 ,5 )# and #(4 ,9 )#. If the triangle's area is #6 #, what are the lengths of the triangle's sides?

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Answer 1 · 2018-06-02T12:31:40

Lengths of three sides are #color(brown)(5, 3.47, 3.47#

Given : #(x_b,y_b) = (7,5), (x_c,y_c) = (4,9), A_t = 6#

#a = sqrt((7-4)^2 + (5-9)^2) = 5#

Altitudes #h = (2 * A_t) / a = (2 * 6)/5 = 2.4#

#b = c = sqrt((a/2)^2 + h^2) = sqrt(2.5^2 + 2.4^2) = 3.47#