Two corners of an isosceles triangle are at $(6, 4)$ $(6 ,4 )$ and $(2, 7)$ $(2 ,7 )$ . If the triangle's area is $36$ $36$ , what are the lengths of the triangle's sides?

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Answer 1 · 2018-06-02T08:52:07

Length of the sides are $5, 14.59, 14.59$ $color(blue)(5, 14.59, 14.59$

Area of triangle $A_{t} = (\frac{1}{2}) a h$ $A_t = (1/2) a h$

Given $(x_{b}, y_{b}) = (6, 4), (x_{c}, y_{c}) = (2, 7), A_{t} \equiv 36$ $(x_b, y_b ) = (6,4), (x_c,y_c) = (2,7), A_t -= 36$

$a = \sqrt{{(6 - 2)}^{2} + {(4 - 7)}^{2}} = 5$ $a = sqrt((6-2)^2 + (4-7)^2) = 5$

$h = \frac{2 \cdot A_{t}}{a} = \frac{2 \cdot 36}{5} = 14.5$ $h = (2 * A_t)/a = (2*36)/5= 14.5$

$b = c = \sqrt{{(\frac{5}{2})}^{2} + {14.5}^{2}} = 14.59$ $b = c = sqrt((5/2)^2 + 14.5^2 )= 14.59$

Two corners of an isosceles triangle are at (6,4)(6 ,4 ) and (2,7)(2 ,7 ). If the triangle's area is 3636 , what are the lengths of the triangle's sides?