Two corners of an isosceles triangle are at #(6 ,3 )# and #(4 ,8 )#. If the triangle's area is #8 #, what are the lengths of the triangle's sides?

Question

1119 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-09T04:50:20

Lengths of the three sides are #color(blue)(5.3852, 3.8752, 3.8752)#

enter image source here

Given #B(6,3), C(4,8), A_t = 8#

#BC = color(red)(a ) = sqrt((4-6)^2 + (8-3)^2) = color(red)(5.3852)#

#AD = h = (2 * A_t ) / a = (2 * 8) / 5.3852 = color(red)(2.9711)#

#AC = AB = b = c = sqrt((a/2)^2 + h^2) = sqrt((5.3852/2)^2 + 2.7911^2)#

#color(red)(b = 3.8782)#

Lengths of the three sides are #color(blue)(5.3852, 3.8752, 3.8752)#