Two corners of an isosceles triangle are at $(2, 9)$ $(2 ,9 )$ and $(6, 7)$ $(6 ,7 )$ . If the triangle's area is $4$ $4$ , what are the lengths of the triangle's sides?

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Two corners of an isosceles triangle are at $(2, 9)$ $(2 ,9 )$ and $(6, 7)$ $(6 ,7 )$ . If the triangle's area is $4$ $4$ , what are the lengths of the triangle's sides?

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Answer 1 · 2017-07-30T11:30:46

The length of three sides of triangle are $4.47, 2.86, 2.86$ $4.47 ,2.86 , 2.86$ unit.

Explanation:

Base of the isocelles triangle is $B = \sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}) = \sqrt{{(6 - 2)}^{2} + {(7 - 9)}^{2}}) = \sqrt{16 + 4} = \sqrt{20} \approx 4.47 (2 d p)$ $B= sqrt((x_2-x_1)^2+(y_2-y_1)^2)) = sqrt((6-2)^2+(7-9)^2)) =sqrt(16+4)=sqrt20 ~~4.47(2dp)$ unit

We know area of triangle is $A_{t} = \frac{1}{2} \cdot B \cdot H$ $A_t =1/2*B*H$ Where $H$ $H$ is altitude.
$:. 4=1/2*4.47*H or H= 8/4.47 ~~1.79(2dp)$ unit

Legs are $L = sqrt(H^2+(B/2)^2)= sqrt( 1.79^2+(4.47/2)^2) ~~2.86(2dp)$ unit

The length of three sides of triangle are $4.47 ,2.86 , 2.86$ unit [Ans]

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Two corners of an isosceles triangle are at $(2, 9)$ $(2 ,9 )$ and $(6, 7)$ $(6 ,7 )$ . If the triangle's area is $4$ $4$ , what are the lengths of the triangle's sides?

1 Answer

Explanation:

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Two corners of an isosceles triangle are at (2 ,9 )(2,9)(2 ,9 ) and (6 ,7 )(6,7)(6 ,7 ). If the triangle's area is 4 44 , what are the lengths of the triangle's sides?

1 Answer

Explanation:

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Two corners of an isosceles triangle are at $(2, 9)$ $(2 ,9 )$ and $(6, 7)$ $(6 ,7 )$ . If the triangle's area is $4$ $4$ , what are the lengths of the triangle's sides?