Two corners of an isosceles triangle are at #(4 ,3 )# and #(9 ,5 )#. If the triangle's area is #64 #, what are the lengths of the triangle's sides?

1 Answer
Dec 11, 2017

Measure of the three sides are (5.3852, 23.9208, 24.9208)

Explanation:

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Length #a = sqrt((9-4)^2 + (5-3)^2) = sqrt 29 = 5.3852#

Area of #Delta = 64#
#:. h = (Area) / (a/2) = 64 / (5.3852/2) = 64 / 2.6926 = 23.7688#
#side b = sqrt((a/2)^2 + h^2) = sqrt((2.6926)^2 + (23.7688)^2)#
#b = 23.9208#

Since the triangle is isosceles, third side is also #= b = 23.9208#

Measure of the three sides are (5.3852, 23.9208, 23.9208)