Two corners of an isosceles triangle are at #(2 ,9 )# and #(7 ,5 )#. If the triangle's area is #4 #, what are the lengths of the triangle's sides?

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Answer 1 · 2017-12-05T09:37:47

The three sides are #color(blue)(6.4031, 3.4367, 3.4367)#

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Length #a = sqrt((7-2)^2 + (5-9)^2) = sqrt41 = 6.4031#

Area of #Delta = 4#
#:. h = (Area) / (a/2) = 4 / (6.4031/2) = 4/3.2016 = 1.2494#

#side b = sqrt((a/2)^2 + h^2) = sqrt((3.2016)^2 + (1.2494)^2)#
#b = 3.4367#

Since the triangle is isosceles, third side is also #= b = 3.4367#