Two corners of an isosceles triangle are at $(8, 5)$ $(8 ,5 )$ and $(6, 1)$ $(6 ,1 )$ . If the triangle's area is $12$ $12$ , what are the lengths of the triangle's sides?

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Answer 1 · 2017-12-05T10:34:45

Measure of the three sides of the $Delta$ are $color(red)(4.4721, 2.8636, 2.8636$

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Length $a = sqrt((6-8)^2 + (1-5)^2) = sqrt 20 = 4.4721$

Area of $Delta = 12$
$:. h = (Area) / (a/2) = 12 / (4.4721/2) = 4/2.2361 = 1.7888$

$side b = sqrt((a/2)^2 + h^2) = sqrt((2.2361)^2 + (1.7888)^2)$
$b = 2.8636$

Since the triangle is isosceles, third side is also $= b = 2.8636$

Two corners of an isosceles triangle are at (8 ,5 )(8,5)(8 ,5 ) and (6 ,1 )(6,1)(6 ,1 ). If the triangle's area is 12 1212 , what are the lengths of the triangle's sides?