Two corners of an isosceles triangle are at $(1 ,2 )$ and $(9 ,7 )$ . If the triangle's area is $64$ , what are the lengths of the triangle's sides?

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Answer 1 · 2017-12-05T11:42:35

Lengths of the three sides of the $Delta$ are $color(blue)(9.434, 14.3645, 14.3645)$

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Length $a = sqrt((9-1)^2 + (7-2)^2) = sqrt 89 = 9.434$

Area of $Delta = 4$
$:. h = (Area) / (a/2) =6 4 / (9.434/2) =6 4/4.717 = 13.5679$

$side b = sqrt((a/2)^2 + h^2) = sqrt((4.717)^2 + (13.5679)^2)$
$b = 14.3645$

Since the triangle is isosceles, third side is also $= b = 14.3645$

Two corners of an isosceles triangle are at (1 ,2 )(1 ,2 ) and (9 ,7 )(9 ,7 ). If the triangle's area is 64 64 , what are the lengths of the triangle's sides?