Two corners of an isosceles triangle are at $(8, 5)$ $(8 ,5 )$ and $(9, 1)$ $(9 ,1 )$ . If the triangle's area is $12$ $12$ , what are the lengths of the triangle's sides?

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Two corners of an isosceles triangle are at $(8, 5)$ $(8 ,5 )$ and $(9, 1)$ $(9 ,1 )$ . If the triangle's area is $12$ $12$ , what are the lengths of the triangle's sides?

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Answer 1 · 2018-07-23T02:55:52

$Lengths of the triangle a = \sqrt{17}, b = \sqrt{\frac{2593}{68}}, c = \sqrt{\frac{2593}{68}}$ $color(maroon)("Lengths of the triangle "a = sqrt 17, b = sqrt(2593 / 68), c = sqrt(2593 / 68)$

Explanation:

![https://study.com/academy/lesson/http://what-is-an-isosceles-triangle-definition-properties-theorem.html](https://useruploads.socratic.org/XySDJrnQXi74AH1iJi5s_isosceles.png)

$B (8, 5), C (9, 1), A_{t} = 12$ $color(red)( B(8,5), C(9,1), A_t = 12$

let $¯ ¯¯¯¯ ¯ A D = h$ $bar(AD) = h$

$¯ ¯¯¯¯ ¯ B C = a = \sqrt{{(9 - 8)}^{2} + {(1 - 5)}^{2}} = \sqrt{17}$ $bar(BC) = a = sqrt((9-8)^2 + (1-5)^2) = sqrt17$

$A r e a o f △ A_{t} = 12 = (\frac{1}{2}) a \cdot h = \frac{\sqrt{17} h}{2}$ $Area of triangle " A_t = 12 = (1/2) a *h = (sqrt17 h)/2$

$h = \frac{24}{\sqrt{17}}$ $h = 24 / sqrt17$

$¯ ¯¯¯¯ ¯ A C = ¯ ¯¯¯¯ ¯ A B = b = \sqrt{{(\frac{a}{2})}^{2} + h^{2}}$ $bar(AC) = bar(AB) = b = sqrt((a/2)^2 + h^2)$

$b = \sqrt{{(\frac{\sqrt{17}}{2})}^{2} + {(\frac{24}{\sqrt{17}})}^{2}}$ $b = sqrt((sqrt17/2)^2 + (24/sqrt17)^2)$

$b = \sqrt{\frac{17}{4} + \frac{576}{17}} = \sqrt{\frac{2593}{68}}$ $b = sqrt(17/4 + 576/17) = sqrt(2593/68)$

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Two corners of an isosceles triangle are at $(8, 5)$ $(8 ,5 )$ and $(9, 1)$ $(9 ,1 )$ . If the triangle's area is $12$ $12$ , 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 (8,5)(8 ,5 ) and (9,1)(9 ,1 ). If the triangle's area is 1212 , what are the lengths of the triangle's sides?

1 Answer

Explanation:

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Two corners of an isosceles triangle are at $(8, 5)$ $(8 ,5 )$ and $(9, 1)$ $(9 ,1 )$ . If the triangle's area is $12$ $12$ , what are the lengths of the triangle's sides?