Two corners of an isosceles triangle are at $(4, 9)$ $(4 ,9 )$ and $(9, 3)$ $(9 ,3 )$ . If the triangle's area is $64$ $64$ , what are the lengths of the triangle's sides?

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Two corners of an isosceles triangle are at $(4, 9)$ $(4 ,9 )$ and $(9, 3)$ $(9 ,3 )$ . If the triangle's area is $64$ $64$ , what are the lengths of the triangle's sides?

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Answer 1 · 2016-02-11T17:36:32

enter image source here The sides are:
Base, $b = ¯ ¯¯¯¯ ¯ A B = 7.8$ $b = bar(AB) = 7.8$
Equal sides, $¯ ¯¯¯¯ ¯ A C = ¯ ¯¯¯¯ ¯ B C = 16.8$ $bar(AC) = bar(BC) = 16.8$

Explanation:

$A_Delta = 1/2 bh = 64$
Using the distance formula find b...
$b = sqrt((x_2-x_1)^2 + (y_2 - y_1)^2)$
$x_1 = 4; x_2 = 9; y_1 = 9; y_2 = 3$
substitute and find h:
$b = sqrt(25 + 36) = sqrt(61) ~~ 7.81$
$h = 2(64)/sqrt(61) = 16.4$
Now using Pythagoras theorem find the sides, $barAC$ :
$barAC = sqrt(61/4 + 128^2/61) = sqrt((3,721 + 65,536)/2) = 16.8$

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Two corners of an isosceles triangle are at $(4, 9)$ $(4 ,9 )$ and $(9, 3)$ $(9 ,3 )$ . If the triangle's area is $64$ $64$ , what are the lengths of the triangle's sides?

1 Answer

Explanation:

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Science

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Humanities

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Two corners of an isosceles triangle are at (4 ,9 )(4,9)(4 ,9 ) and (9 ,3 )(9,3)(9 ,3 ). If the triangle's area is 64 6464 , what are the lengths of the triangle's sides?

1 Answer

Explanation:

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Two corners of an isosceles triangle are at $(4, 9)$ $(4 ,9 )$ and $(9, 3)$ $(9 ,3 )$ . If the triangle's area is $64$ $64$ , what are the lengths of the triangle's sides?