Two corners of an isosceles triangle are at #(9 ,4 )# and #(3 ,8 )#. If the triangle's area is #48 #, what are the lengths of the triangle's sides?

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Answer 1 · 2017-12-05T10:25:30

Three sides of the triangle are #color(blue)(6.4031, 15.3305, 15.3305)#

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Length #a = sqrt((3-9)^2 + (8-4)^2) = sqrt41 = 6.4031#

Area of #Delta = 48#
#:. h = (Area) / (a/2) = 48 / (6.4031/2) = 48/3.2016 = 14.9925#

#side b = sqrt((a/2)^2 + h^2) = sqrt((3.2016)^2 + (14.9925)^2)#
#b = 15.3305#

Since the triangle is isosceles, third side is also #= b = 15.3305#