Two corners of an isosceles triangle are at $(1 ,5 )$ and $(6 ,7 )$ . If the triangle's area is $4$ , what are the lengths of the triangle's sides?

Question

1374 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-02T09:22:45

Lengths of the sides are $color(indigo)(5.39, 5.59, 5.59$

Given : $(x_b,y_b) = (1,5), (x_c,y_c) = (6,7), A_t = 4, b = c = ?$

$a = sqrt((7-5)^2 + (6-1)^2) = color(indigo)(5.39$

$h = (2 * A_t) / a = (2 * 4)/5.39 = 1.48$

$b = c = sqrt((a/2)^2 + h^2) = sqrt((5.39/2)^2 + 1.48^2) = color(indigo)(5.59)$

Two corners of an isosceles triangle are at (1 ,5 )(1 ,5 ) and (6 ,7 )(6 ,7 ). If the triangle's area is 4 4 , what are the lengths of the triangle's sides?