Two corners of an isosceles triangle are at $(6, 4)$ $(6 ,4 )$ and $(9, 2)$ $(9 ,2 )$ . If the triangle's area is $36$ $36$ , what are the lengths of the triangle's sides?

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Answer 1 · 2017-12-05T13:10:09

Three sides of the $Delta$ measure (3.6056, 20.0502, 20.0502)

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Length $a = sqrt((9-6)^2 + (2-4)^2) = sqrt13 = 3.6056$

Area of $Delta = 36$
$:. h = (Area) / (a/2) = 36 / (3.6056 /2) = 36 / 1.8028 = 19.969$

$side b = sqrt((a/2)^2 + h^2) = sqrt((1.8028)^2 + (19.969)^2)$
$b = 20.0502$

Since the triangle is isosceles, third side is also $= b = 20.0502$

Two corners of an isosceles triangle are at (6 ,4 )(6,4)(6 ,4 ) and (9 ,2 )(9,2)(9 ,2 ). If the triangle's area is 36 3636 , what are the lengths of the triangle's sides?