Two corners of an isosceles triangle are at $(2, 9)$ $(2 ,9 )$ and $(8, 3)$ $(8 ,3 )$ . If the triangle's area is $9$ $9$ , 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 $(8, 3)$ $(8 ,3 )$ . If the triangle's area is $9$ $9$ , what are the lengths of the triangle's sides?

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Answer 1 · 2017-12-23T12:41:56

The length of three sides of triangle are $8.49, 4.74, 4.74$ $8.49 ,4.74 , 4.74$ unit

Explanation:

Base of the isocelles triangle is

$B = \sqrt{{(x_{1} - x_{2})}_{1}^{2} + {(y_{1} - y_{2})}_{1}^{2}}) = \sqrt{{(2 - 8)}^{2} + {(9 - 3)}^{2}}$ $B= sqrt((x_1-x_2)^2+(y_1-y_2)^2)) = sqrt((2-8)^2+(9-3)^2)$

$= \sqrt{36 + 36} = \sqrt{72} \approx 8.49 (2 d p)$ $=sqrt(36+36)=sqrt72 ~~8.49(2dp)$ 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. $:.9=1/2*8.49*H or H= 18/8.49~~2.12(2dp)$ unit

Legs are $L = sqrt(H^2+(B/2)^2)= sqrt( 2.12^2+(8.49/2)^2)$

$=4.74(2dp)$ unit.

The length of three sides of triangle are $8.49 ,4.74 , 4.74$ unit [Ans]

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Two corners of an isosceles triangle are at $(2, 9)$ $(2 ,9 )$ and $(8, 3)$ $(8 ,3 )$ . If the triangle's area is $9$ $9$ , 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 (8 ,3 )(8,3)(8 ,3 ). If the triangle's area is 9 99 , 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 $(8, 3)$ $(8 ,3 )$ . If the triangle's area is $9$ $9$ , what are the lengths of the triangle's sides?