Two corners of an isosceles triangle are at #(4 ,8 )# and #(1 ,3 )#. If the triangle's area is #5 #, what are the lengths of the triangle's sides?

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Answer 1 · 2017-12-08T11:11:06

Measure of the three sides are (1.715, 2.4201, 2.4201)

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Length #a = sqrt((4-1)^2 + (8-3)^2) = sqrt 34 = 5.831#

Area of #Delta = 5#
#:. h = (Area) / (a/2) = 5 / (5.831/2) = 5 / 2.9155 = 1.715#

#side b = sqrt((a/2)^2 + h^2) = sqrt((2.9155)^2 + (1.715)^2)#
#b = 2.4201#

Since the triangle is isosceles, third side is also #= b = 2.4201#

Measure of the three sides are (1.715, 2.4201, 2.4201)