Two corners of an isosceles triangle are at #(2 ,5 )# and #(4 ,8 )#. If the triangle's area is #6 #, what are the lengths of the triangle's sides?

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Answer 1 · 2018-05-12T04:49:09

#color(green)("lengths of sides of the triangle are " 3.61, 3.77, 3.77#

#A (2,5), C (4,8), " Area of triangle "A_t = 6#

#bar (AC) = b = sqrt((4-2)^2 + (8-5)^2) = sqrt13 = 3.61#

#h = (2 * A_t) / b = (2 * 6) / 3.61 = 3.32#

#a = sqrt(h^2 + (b/2)^2) = sqrt(3.32^2 +( 3.61/2)^2) = 3.77#