Two corners of an isosceles triangle are at #(1 ,2 )# and #(3 ,1 )#. If the triangle's area is #12 #, what are the lengths of the triangle's sides?

1 Answer
Dec 11, 2017

Measure of the three sides are (2.2361, 10.7906, 10.7906)

Explanation:

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Length #a = sqrt((3-1)^2 + (1-2)^2) = sqrt 5 = 2.2361#

Area of #Delta = 12#
#:. h = (Area) / (a/2) = 12 / (2.2361/2) = 12 / 1.1181 = 10.7325#
#side b = sqrt((a/2)^2 + h^2) = sqrt((1.1181)^2 + (10.7325)^2)#
#b = 10.7906#

Since the triangle is isosceles, third side is also #= b = 10.7906#

Measure of the three sides are (2.2361, 10.7906, 10.7906)