Two corners of an isosceles triangle are at $(1, 3)$ $(1 ,3 )$ and $(5, 8)$ $(5 ,8 )$ . If the triangle's area is $8$ $8$ , what are the lengths of the triangle's sides?

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Two corners of an isosceles triangle are at $(1, 3)$ $(1 ,3 )$ and $(5, 8)$ $(5 ,8 )$ . If the triangle's area is $8$ $8$ , what are the lengths of the triangle's sides?

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Answer 1 · 2017-12-15T15:36:22

The length of three sides of triangle are $6.40, 4.06, 4.06$ $6.40 ,4.06 , 4.06$ unit.

Explanation:

Base of the isocelles triangle is

$B = \sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}) = \sqrt{{(5 - 1)}^{2} + {(8 - 3)}^{2}})$ $B= sqrt((x_2-x_1)^2+(y_2-y_1)^2)) = sqrt((5-1)^2+(8-3)^2))$

$= \sqrt{16 + 25} = \sqrt{41} \approx 6.40 (2 d p)$ $=sqrt(16+25)=sqrt41 ~~ 6.40(2dp)$ 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.

$:. 8=1/2*6.40*H or H= 16/6.40 (2dp) ~~ 2.5$ unit.

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

$= sqrt( 2.5^2+(6.40/2)^2)~~4.06(2dp)$ unit

The length of three sides of triangle are $6.40 ,4.06 , 4.06$ unit [Ans]

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Two corners of an isosceles triangle are at $(1, 3)$ $(1 ,3 )$ and $(5, 8)$ $(5 ,8 )$ . If the triangle's area is $8$ $8$ , what are the lengths of the triangle's sides?

1 Answer

Explanation:

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Science

Math

Humanities

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Two corners of an isosceles triangle are at (1 ,3 )(1,3)(1 ,3 ) and (5 ,8 )(5,8)(5 ,8 ). If the triangle's area is 8 88 , what are the lengths of the triangle's sides?

1 Answer

Explanation:

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Two corners of an isosceles triangle are at $(1, 3)$ $(1 ,3 )$ and $(5, 8)$ $(5 ,8 )$ . If the triangle's area is $8$ $8$ , what are the lengths of the triangle's sides?