Two corners of an isosceles triangle are at $(7, 2)$ $(7 ,2 )$ and $(4, 9)$ $(4 ,9 )$ . If the triangle's area is $24$ $24$ , what are the lengths of the triangle's sides?

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Two corners of an isosceles triangle are at $(7, 2)$ $(7 ,2 )$ and $(4, 9)$ $(4 ,9 )$ . If the triangle's area is $24$ $24$ , what are the lengths of the triangle's sides?

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Answer 1 · 2017-10-26T11:27:12

The length of three sides of triangle are $7.62, 7.36, 7.36$ $7.62 ,7.36 , 7.36$ unit

Explanation:

Base of the isocelles triangle is $B = \sqrt{{(x_{1} - x_{2})}_{1}^{2} + {(y_{1} - y_{2})}_{1}^{2}})$ $B= sqrt((x_1-x_2)^2+(y_1-y_2)^2))$

$= \sqrt{{(7 - 4)}^{2} + {(2 - 9)}^{2}}) = \sqrt{9 + 49} = \sqrt{58} \approx 7.62 (2 d p)$ $= sqrt((7-4)^2+(2-9)^2)) =sqrt(9+49)=sqrt58 ~~7.62(2dp)$ 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.

$:. 24=1/2*7.62*H or H~~ 48/7.62 ~~ 6.30(2dp)$ unit

Legs are $L = sqrt(H^2+(B/2)^2)$

$= sqrt( 6.30^2+(7.62/2)^2) ~~7.36(2dp)$ unit

The length of three sides of triangle are $7.62 ,7.36 , 7.36$ unit [Ans]

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Two corners of an isosceles triangle are at $(7, 2)$ $(7 ,2 )$ and $(4, 9)$ $(4 ,9 )$ . If the triangle's area is $24$ $24$ , what are the lengths of the triangle's sides?

1 Answer

Explanation:

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Humanities

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Two corners of an isosceles triangle are at (7 ,2 )(7,2)(7 ,2 ) and (4 ,9 )(4,9)(4 ,9 ). If the triangle's area is 24 2424 , what are the lengths of the triangle's sides?

1 Answer

Explanation:

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Two corners of an isosceles triangle are at $(7, 2)$ $(7 ,2 )$ and $(4, 9)$ $(4 ,9 )$ . If the triangle's area is $24$ $24$ , what are the lengths of the triangle's sides?