Two corners of an isosceles triangle are at $(4, 3)$ $(4 ,3 )$ and $(9, 5)$ $(9 ,5 )$ . 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 $(4, 3)$ $(4 ,3 )$ and $(9, 5)$ $(9 ,5 )$ . If the triangle's area is $64$ $64$ , what are the lengths of the triangle's sides?

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Answer 1 · 2017-12-11T08:18:40

Measure of the three sides are (5.3852, 23.9208, 24.9208)

Explanation:

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Length $a = \sqrt{{(9 - 4)}^{2} + {(5 - 3)}^{2}} = \sqrt{29} = 5.3852$ $a = sqrt((9-4)^2 + (5-3)^2) = sqrt 29 = 5.3852$

Area of $Delta = 64$
$:. h = (Area) / (a/2) = 64 / (5.3852/2) = 64 / 2.6926 = 23.7688$
$side b = sqrt((a/2)^2 + h^2) = sqrt((2.6926)^2 + (23.7688)^2)$
$b = 23.9208$

Since the triangle is isosceles, third side is also $= b = 23.9208$

Measure of the three sides are (5.3852, 23.9208, 23.9208)

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Two corners of an isosceles triangle are at $(4, 3)$ $(4 ,3 )$ and $(9, 5)$ $(9 ,5 )$ . 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

Math

Humanities

... and beyond

Two corners of an isosceles triangle are at (4 ,3 )(4,3)(4 ,3 ) and (9 ,5 )(9,5)(9 ,5 ). 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 $(4, 3)$ $(4 ,3 )$ and $(9, 5)$ $(9 ,5 )$ . If the triangle's area is $64$ $64$ , what are the lengths of the triangle's sides?