Question

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?

Answer 1

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

Explanation:

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]