Two corners of an isosceles triangle are at #(2 ,4 )# and #(3 ,8 )#. If the triangle's area is #64 #, what are the lengths of the triangle's sides?

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Answer 1 · 2017-12-05T13:23:41

Measure of the three sides are (4.1231, 31.1122, 31.1122)

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Length #a = sqrt((3-2)^2 + (8-4)^2) = sqrt 17 = 4.1231#

Area of #Delta = 64#
#:. h = (Area) / (a/2) = 64 / (4.1231/2) = 64 / 2.0616 = 31.0438#

#side b = sqrt((a/2)^2 + h^2) = sqrt((2.0616)^2 + (31.0438)^2)#
#b = 31.1122

Since the triangle is isosceles, third side is also #= b = 31.1122#