Two corners of an isosceles triangle are at #(6 ,4 )# and #(9 ,2 )#. If the triangle's area is #36 #, what are the lengths of the triangle's sides?

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Answer 1 · 2017-12-05T13:10:09

Three sides of the #Delta# measure (3.6056, 20.0502, 20.0502)

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Length #a = sqrt((9-6)^2 + (2-4)^2) = sqrt13 = 3.6056#

Area of #Delta = 36#
#:. h = (Area) / (a/2) = 36 / (3.6056 /2) = 36 / 1.8028 = 19.969#

#side b = sqrt((a/2)^2 + h^2) = sqrt((1.8028)^2 + (19.969)^2)#
#b = 20.0502#

Since the triangle is isosceles, third side is also #= b = 20.0502#