Two corners of an isosceles triangle are at #(2 ,5 )# and #(9 ,4 )#. If the triangle's area is #12 #, what are the lengths of the triangle's sides?

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Answer 1 · 2017-12-05T11:50:32

Lengths of the three sides of the #Delta# are #color(blue )(7.0711, 4.901, 4.901)#

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Length #a = sqrt((9-2)^2 + (4-5)^2) = sqrt50 = 7.0711#

Area of #Delta = 12#
#:. h = (Area) / (a/2) = 12 / (7.0711/2) = 12 / 3.5355 = 3.3941#

#side b = sqrt((a/2)^2 + h^2) = sqrt((3.5355)^2 + (3.3941)^2)#
#b = 4.901#

Since the triangle is isosceles, third side is also #= b = 4.901#