Question

Two corners of an isosceles triangle are at `(7 ,5 )` and `(3 ,9 )`. If the triangle's area is `6`, what are the lengths of the triangle's sides?

Answer 1

The length of three sides of triangle are `5.66 ,3.54 , 3.54` unit

Explanation:

Base of the isocelles triangle is `B= sqrt((x_2-x_1)^2+(y_2-y_1)^2)) = sqrt((3-7)^2+(9-5)^2)) =sqrt(16+16)=sqrt32 =5.66(2dp)`unit

We know area of triangle is `A_t =1/2*B*H` Where `H` is altitude.
`:. 6=1/2*5.66*H or H= 12/5.66=2.12(2dp)`unit

Legs are `L = sqrt(H^2+(B/2)^2)= sqrt( 2.12^2+(5.66/2)^2)=3.54(2dp)`unit

The length of three sides of triangle are `5.66 ,3.54 , 3.54` unit [Ans]