Two corners of an isosceles triangle are at $(6, 3)$ $(6 ,3 )$ and $(4, 8)$ $(4 ,8 )$ . If the triangle's area is $8$ $8$ , what are the lengths of the triangle's sides?

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Two corners of an isosceles triangle are at $(6, 3)$ $(6 ,3 )$ and $(4, 8)$ $(4 ,8 )$ . If the triangle's area is $8$ $8$ , what are the lengths of the triangle's sides?

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Answer 1 · 2018-01-09T04:50:20

Lengths of the three sides are $5.3852, 3.8752, 3.8752$ $color(blue)(5.3852, 3.8752, 3.8752)$

Explanation:

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Given $B (6, 3), C (4, 8), A_{t} = 8$ $B(6,3), C(4,8), A_t = 8$

$B C = a = \sqrt{{(4 - 6)}^{2} + {(8 - 3)}^{2}} = 5.3852$ $BC = color(red)(a ) = sqrt((4-6)^2 + (8-3)^2) = color(red)(5.3852)$

$A D = h = \frac{2 \cdot A_{t}}{a} = \frac{2 \cdot 8}{5.3852} = 2.9711$ $AD = h = (2 * A_t ) / a = (2 * 8) / 5.3852 = color(red)(2.9711)$

$A C = A B = b = c = \sqrt{{(\frac{a}{2})}^{2} + h^{2}} = \sqrt{{(\frac{5.3852}{2})}^{2} + {2.7911}^{2}}$ $AC = AB = b = c = sqrt((a/2)^2 + h^2) = sqrt((5.3852/2)^2 + 2.7911^2)$

$b = 3.8782$ $color(red)(b = 3.8782)$

Lengths of the three sides are $5.3852, 3.8752, 3.8752$ $color(blue)(5.3852, 3.8752, 3.8752)$

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Two corners of an isosceles triangle are at $(6, 3)$ $(6 ,3 )$ and $(4, 8)$ $(4 ,8 )$ . If the triangle's area is $8$ $8$ , what are the lengths of the triangle's sides?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

Two corners of an isosceles triangle are at (6 ,3 )(6,3)(6 ,3 ) and (4 ,8 )(4,8)(4 ,8 ). If the triangle's area is 8 88 , what are the lengths of the triangle's sides?

1 Answer

Explanation:

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Two corners of an isosceles triangle are at $(6, 3)$ $(6 ,3 )$ and $(4, 8)$ $(4 ,8 )$ . If the triangle's area is $8$ $8$ , what are the lengths of the triangle's sides?