Two corners of an isosceles triangle are at $(4, 8)$ $(4 ,8 )$ and $(1, 3)$ $(1 ,3 )$ . If the triangle's area is $5$ $5$ , what are the lengths of the triangle's sides?

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Answer 1 · 2017-12-08T11:11:06

Measure of the three sides are (1.715, 2.4201, 2.4201)

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Length $a = \sqrt{{(4 - 1)}^{2} + {(8 - 3)}^{2}} = \sqrt{34} = 5.831$ $a = sqrt((4-1)^2 + (8-3)^2) = sqrt 34 = 5.831$

Area of $Delta = 5$
$:. h = (Area) / (a/2) = 5 / (5.831/2) = 5 / 2.9155 = 1.715$

$side b = sqrt((a/2)^2 + h^2) = sqrt((2.9155)^2 + (1.715)^2)$
$b = 2.4201$

Since the triangle is isosceles, third side is also $= b = 2.4201$

Measure of the three sides are (1.715, 2.4201, 2.4201)

Two corners of an isosceles triangle are at (4 ,8 )(4,8)(4 ,8 ) and (1 ,3 )(1,3)(1 ,3 ). If the triangle's area is 5 55 , what are the lengths of the triangle's sides?