Two corners of an isosceles triangle are at #(4 ,2 )# 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 · 2017-12-28T05:46:45

Measure of the three sides are 5.099, 3.4696, 3.4696

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Length of the base #a = sqrt((5-4)^2 + (7-2)^2) = 5.099#

Given area #= 3 = (1/2) * a * h#

#:. h = 6 / (5.099 /2) = 2.3534#

Length of one of the equal sides of the isosceles triangle is
# b = sqrt((a/2)^2 + h^2) = sqrt((5.099/2)^2 + (2.3534)^2) = 3.4696#

Lengths of the isosceles triangle are 5.099, 3.4696, 3.4696