Two corners of an isosceles triangle are at $(2, 5)$ $(2 ,5 )$ and $(9, 8)$ $(9 ,8 )$ . If the triangle's area is $6$ $6$ , what are the lengths of the triangle's sides?

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Two corners of an isosceles triangle are at $(2, 5)$ $(2 ,5 )$ and $(9, 8)$ $(9 ,8 )$ . If the triangle's area is $6$ $6$ , what are the lengths of the triangle's sides?

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Answer 1 · 2016-03-06T15:00:52

1.) $\sqrt{58}$ $sqrt58$ , $\sqrt{58}$ $" " "sqrt58$ , $2 \sqrt{29 + \sqrt{805}}$ $" " "2sqrt(29+sqrt(805))$
2.) $\sqrt{58} = 7.615$ $sqrt58=7.615$ , $\sqrt{58} = 7.615$ $" " "sqrt58=7.615$ , $2 \sqrt{29 - \sqrt{805}} = 1.58427$ $" " "2sqrt(29-sqrt(805))=1.58427$
3.) $\sqrt{58} = 7.615$ $sqrt58=7.615$ , $\frac{\sqrt{57130}}{58} = 4.12101$ $sqrt(57130)/58=4.12101$ , $\frac{\sqrt{57130}}{58} = 4.12101$ $sqrt(57130)/58=4.12101$

Explanation:

The possible triangles are when the given distance $\sqrt{58}$ $sqrt58$ are the two equal sides

triangle 1: the coordinates are $(2, 5), (9, 8), (\frac{279 + 7 \sqrt{805}}{29}, \frac{190 + 3 \sqrt{805}}{29})$ $(2,5), (9,8), ((279+7sqrt805)/29,(190+3sqrt805)/29)$

triangle 2: the coordinates are $(2, 5), (9, 8), (\frac{279 - 7 \sqrt{805}}{29}, \frac{190 - 3 \sqrt{805}}{29})$ $(2, 5), (9, 8), ((279-7sqrt805)/29,(190-3sqrt805)/29)$

For the 3rd triangle, $\sqrt{58}$ $sqrt58$ is the 3rd side and is not congruent to any side.
triangle 3: the coordinates are $(2, 5), (9, 8), (\frac{355}{58}, \frac{293}{58})$ $(2, 5), (9, 8), (355/58, 293/58)$

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Two corners of an isosceles triangle are at $(2, 5)$ $(2 ,5 )$ and $(9, 8)$ $(9 ,8 )$ . If the triangle's area is $6$ $6$ , what are the lengths of the triangle's sides?

1 Answer

Explanation:

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Two corners of an isosceles triangle are at (2,5)(2 ,5 ) and (9,8)(9 ,8 ). If the triangle's area is 66 , what are the lengths of the triangle's sides?

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Two corners of an isosceles triangle are at $(2, 5)$ $(2 ,5 )$ and $(9, 8)$ $(9 ,8 )$ . If the triangle's area is $6$ $6$ , what are the lengths of the triangle's sides?