Two corners of an isosceles triangle are at $(2 ,5 )$ and $(9 ,4 )$ . If the triangle's area is $12$ , what are the lengths of the triangle's sides?

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Answer 1 · 2017-12-05T11:50:32

Lengths of the three sides of the $Delta$ are $color(blue )(7.0711, 4.901, 4.901)$

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Length $a = sqrt((9-2)^2 + (4-5)^2) = sqrt50 = 7.0711$

Area of $Delta = 12$
$:. h = (Area) / (a/2) = 12 / (7.0711/2) = 12 / 3.5355 = 3.3941$

$side b = sqrt((a/2)^2 + h^2) = sqrt((3.5355)^2 + (3.3941)^2)$
$b = 4.901$

Since the triangle is isosceles, third side is also $= b = 4.901$

Two corners of an isosceles triangle are at (2 ,5 )(2 ,5 ) and (9 ,4 )(9 ,4 ). If the triangle's area is 12 12 , what are the lengths of the triangle's sides?