Two corners of an isosceles triangle are at $(8 ,5 )$ and $(3 ,2 )$ . If the triangle's area is $4$ , what are the lengths of the triangle's sides?

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Answer 1 · 2017-04-06T11:05:13

The length of three sides of triangle are $5.83 , 3.22 , 3.22$ unit

Base of the isocelles triangle is $B= sqrt((x_1-x_2)^2+(y_1-y_2)^2)) = sqrt((8-3)^2+(5-2)^2)) =sqrt(25+9)=sqrt 34 ~~5.83(2dp)$ unit

We know area of triangle is $A_t =1/2*B*H$ Where $H$ is altitude.
$:. 4=1/2*5.83*H or H= 8/5.83 ~~1.37(2dp)$ unit

Legs are $L = sqrt(H^2+(B/2)^2)= sqrt( 1.37^2+(5.83/2)^2) ~~3.22(2dp)$ unit

The length of three sides of triangle are $5.83 , 3.22 , 3.22$ unit [Ans]

Two corners of an isosceles triangle are at (8 ,5 )(8 ,5 ) and (3 ,2 )(3 ,2 ). If the triangle's area is 4 4 , what are the lengths of the triangle's sides?