Two corners of an isosceles triangle are at #(1 ,2 )# and #(9 ,7 )#. If the triangle's area is #64 #, what are the lengths of the triangle's sides?

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Answer 1 · 2017-12-05T11:42:35

Lengths of the three sides of the #Delta# are #color(blue)(9.434, 14.3645, 14.3645)#

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Length #a = sqrt((9-1)^2 + (7-2)^2) = sqrt 89 = 9.434#

Area of #Delta = 4#
#:. h = (Area) / (a/2) =6 4 / (9.434/2) =6 4/4.717 = 13.5679 #

#side b = sqrt((a/2)^2 + h^2) = sqrt((4.717)^2 + (13.5679)^2)#
#b = 14.3645#

Since the triangle is isosceles, third side is also #= b = 14.3645#