Two corners of an isosceles triangle are at #(1 ,6 )# and #(2 ,7 )#. If the triangle's area is #36 #, what are the lengths of the triangle's sides?

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Answer 1 · 2017-12-08T11:00:07

Measure of the three sides are (1.414, 51.4192, 51.4192)

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Length #a = sqrt((2-1)^2 + (7-6)^2) = sqrt 2 = 1.414#

Area of #Delta = 12#
#:. h = (Area) / (a/2) = 36 / (1.414/2) = 36 / 0.707 = 50.9194#

#side b = sqrt((a/2)^2 + h^2) = sqrt((0.707)^2 + (50.9194)^2)#
#b = 51.4192

Since the triangle is isosceles, third side is also #= b = 51.4192#

Measure of the three sides are (1.414, 51.4192, 51.4192)