Two corners of an isosceles triangle are at $(9 ,6 )$ and $(4 ,2 )$ . If the triangle's area is $64$ , what are the lengths of the triangle's sides?

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Answer 1 · 2018-06-02T08:42:02

Lengths of the sides are $color (crimson)(6.41,20.26,20.26$

Let the sides be a, b, c with b = c.

$a = sqrt((9-4)^2 + (6-2)^2) = 6.41$

$h = (2 * A_t) / a = (2*64)/sqrt(41) = 20$

$b = c = sqrt((a/2)^2 + h^2) = sqrt((6.41/2)^2 + 20^2) = 20.26$

Lengths of the sides are $color (crimson)(6.41,20.26,20.26$

Two corners of an isosceles triangle are at (9 ,6 )(9 ,6 ) and (4 ,2 )(4 ,2 ). If the triangle's area is 64 64 , what are the lengths of the triangle's sides?