Two corners of an isosceles triangle are at #(4 ,8 )# and #(5 ,7 )#. If the triangle's area is #3 #, what are the lengths of the triangle's sides?

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Answer 1 · 2017-12-08T11:05:01

Measure of the three sides are (1.414, 4.3018, 4.3018)

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Length #a = sqrt((5-4)^2 + (7-8)^2) = sqrt 37 = 1.414#

Area of #Delta = 12#
#:. h = (Area) / (a/2) = 3 / (1.414/2) = 3 / 0.707 = 4.2433#

#side b = sqrt((a/2)^2 + h^2) = sqrt((0.707)^2 + (4.2433)^2)#
#b = 4.3018#

Since the triangle is isosceles, third side is also #= b = 4.3018#

Measure of the three sides are (1.414, 4.3018, 4.3018)