Question

Two corners of an isosceles triangle are at `(8 ,5 )` and `(6 ,1 )`. If the triangle's area is `15`, what are the lengths of the triangle's sides?

Answer 1

The length of three sides of triangle are `2sqrt5 ,5sqrt2 ,5sqrt2` unit

Explanation:

Base of the isocelles triangle is `B= sqrt((x_2-x_1)^2+(y_2-y_1)^2)) = sqrt((8-6)^2+(5-1)^2)) =sqrt(4+16)=sqrt20 =2sqrt5`unit

We know area of triangle is `A_t =1/2*B*H` Where `H` is altitude.
`:. 15=1/cancel2*cancel2sqrt5*H or H= 15/sqrt5`unit

Legs are `L = sqrt(H^2+(B/2)^2)= sqrt(( 15/sqrt5)^2+((cancel2sqrt5)/cancel2)^2)=sqrt(45+5) = sqrt 50 = 5sqrt2`unit

The length of three sides of triangle are `2sqrt5 ,5sqrt2 ,5sqrt2` unit [Ans]