Two corners of an isosceles triangle are at #(2 ,4 )# and #(4 ,7 )#. If the triangle's area is #8 #, what are the lengths of the triangle's sides?

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Answer 1 · 2018-05-31T09:34:15

Other two sides are #color(purple)(bar (AB) = bar (BC) = 4.79# long

Area of triangle #A_t = (1/2) b h#

#h = (A_t * 2) / (b)#

Given #A_t = 8, (x_a,y_a) = (2,4), (x_c, y_c) = (4,7)#

#b = bar(AC) = sqrt((4-2)^2 + (7-4)^2) = sqrt(13)#

#h = (2 * 8) / sqrt(13)= 4.44#

Since it’s an isosceles triangle,

#bar (AB) = bar (BC) = sqrt (h^2 + (c/2)^2)#

#=> sqrt((16/sqrt(13))^2 + (sqrt(13)/2)^2)#

#color(purple)(bar (AB) = bar (BC) = 4.79#