Two corners of an isosceles triangle are at #(6 ,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 · 2017-12-20T12:02:18

Lengths of the isosceles triangle are 4.1231, 17.5839, 17.5839

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Length of the base #a = sqrt((7-6)^2 + (2-6)^2) = 4.1231#

Given area #= 36 = (1/2) * a * h#

#:. h = 36 / (4.1231 /2) = 17.4626#

Length of one of the equal sides of the isosceles triangle is
# b = sqrt((a/2)^2 + h^2) = sqrt((4.1231/2)^2 + (17.4626)^2) = 17.5839#

Lengths of the isosceles triangle are 4.1231, 8.17.5839, 17.5839