Two corners of an isosceles triangle are at $(4, 8)$ $(4 ,8 )$ and $(5, 7)$ $(5 ,7 )$ . If the triangle's area is $3$ $3$ , what are the lengths of the triangle's sides?

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Answer 1 · 2017-12-08T11:05:01

Measure of the three sides are (1.414, 4.3018, 4.3018)

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Length $a = \sqrt{{(5 - 4)}^{2} + {(7 - 8)}^{2}} = \sqrt{37} = 1.414$ $a = sqrt((5-4)^2 + (7-8)^2) = sqrt 37 = 1.414$

Area of $Delta = 12$
$:. h = (Area) / (a/2) = 3 / (1.414/2) = 3 / 0.707 = 4.2433$

$side b = sqrt((a/2)^2 + h^2) = sqrt((0.707)^2 + (4.2433)^2)$
$b = 4.3018$

Since the triangle is isosceles, third side is also $= b = 4.3018$

Measure of the three sides are (1.414, 4.3018, 4.3018)

Two corners of an isosceles triangle are at (4 ,8 )(4,8)(4 ,8 ) and (5 ,7 )(5,7)(5 ,7 ). If the triangle's area is 3 33 , what are the lengths of the triangle's sides?