Two corners of an isosceles triangle are at $(7, 5)$ $(7 ,5 )$ and $(4, 9)$ $(4 ,9 )$ . If the triangle's area is $6$ $6$ , what are the lengths of the triangle's sides?

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Answer 1 · 2018-06-02T12:31:40

Lengths of three sides are $5, 3.47, 3.47$ $color(brown)(5, 3.47, 3.47$

Given : $(x_{b}, y_{b}) = (7, 5), (x_{c}, y_{c}) = (4, 9), A_{t} = 6$ $(x_b,y_b) = (7,5), (x_c,y_c) = (4,9), A_t = 6$

$a = \sqrt{{(7 - 4)}^{2} + {(5 - 9)}^{2}} = 5$ $a = sqrt((7-4)^2 + (5-9)^2) = 5$

Altitudes $h = \frac{2 \cdot A_{t}}{a} = \frac{2 \cdot 6}{5} = 2.4$ $h = (2 * A_t) / a = (2 * 6)/5 = 2.4$

$b = c = \sqrt{{(\frac{a}{2})}^{2} + h^{2}} = \sqrt{{2.5}^{2} + {2.4}^{2}} = 3.47$ $b = c = sqrt((a/2)^2 + h^2) = sqrt(2.5^2 + 2.4^2) = 3.47$

Two corners of an isosceles triangle are at (7,5)(7 ,5 ) and (4,9)(4 ,9 ). If the triangle's area is 66 , what are the lengths of the triangle's sides?