Two corners of an isosceles triangle are at $(2, 9)$ $(2 ,9 )$ and $(7, 5)$ $(7 ,5 )$ . If the triangle's area is $4$ $4$ , what are the lengths of the triangle's sides?

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Answer 1 · 2017-12-05T09:37:47

The three sides are $6.4031, 3.4367, 3.4367$ $color(blue)(6.4031, 3.4367, 3.4367)$

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Length $a = \sqrt{{(7 - 2)}^{2} + {(5 - 9)}^{2}} = \sqrt{41} = 6.4031$ $a = sqrt((7-2)^2 + (5-9)^2) = sqrt41 = 6.4031$

Area of $Delta = 4$
$:. h = (Area) / (a/2) = 4 / (6.4031/2) = 4/3.2016 = 1.2494$

$side b = sqrt((a/2)^2 + h^2) = sqrt((3.2016)^2 + (1.2494)^2)$
$b = 3.4367$

Since the triangle is isosceles, third side is also $= b = 3.4367$

Two corners of an isosceles triangle are at (2 ,9 )(2,9)(2 ,9 ) and (7 ,5 )(7,5)(7 ,5 ). If the triangle's area is 4 44 , what are the lengths of the triangle's sides?