Question

Two corners of an isosceles triangle are at `(2 ,9 )` and `(6 ,7 )`. 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 `4.47 ,2.86 , 2.86` unit.

Explanation:

Base of the isocelles triangle is `B= sqrt((x_2-x_1)^2+(y_2-y_1)^2)) = sqrt((6-2)^2+(7-9)^2)) =sqrt(16+4)=sqrt20 ~~4.47(2dp)`unit

We know area of triangle is `A_t =1/2*B*H` Where `H` is altitude.
`:. 4=1/2*4.47*H or H= 8/4.47 ~~1.79(2dp)`unit

Legs are `L = sqrt(H^2+(B/2)^2)= sqrt( 1.79^2+(4.47/2)^2) ~~2.86(2dp)`unit

The length of three sides of triangle are `4.47 ,2.86 , 2.86` unit [Ans]