Question

Two corners of an isosceles triangle are at `(5 ,2 )` and `(2 ,1 )`. If the triangle's area is `3`, what are the lengths of the triangle's sides?

Answer 1

Three sides of triangle are `3.16(2dp), 2.47(2dp) ,2.47(2dp)` unit.

Explanation:

The base of the isosceles triangle, `b=sqrt( (x_1-x_2)^2+(y_1-y_2)^2) = sqrt( (5-2)^2+(2-1)^2) =sqrt10=3.16(2dp)unit`

The area of the isosceles triangle is `A_t = 1/2 * b *h =1/2*3.16 *h ; A_t=3 :. h = (2* A_t )/b = (2*3)/3.16=6/3.16= 1.90(2dp) unit`. Where `h` is the altitude of triangle.

The legs of the isosceles triangle are `l_1=l_2= sqrt(h^2+(b/2)^2)=sqrt(1.9^2+(3.16/2)^2) =2.47(2dp) unit`

Hence the length of three sides of triangle are `3.16(2dp), 2.47(2dp) ,2.47(2dp)` unit [Ans]