# Finding length of triangle sides giving answer in terms of surds

For the question "The corners of a triangle are the points P(4,7), Q(-2,5) and R(3, -10). Find the length of each side of triangle PQR, giving your answers in terms of surds".

is the answer: PQ = 2 square root 10 PR = square root 290 RQ = 5 square root 10 Thanks.

the distance between two points is $$L=\sqrt{(y_1-y_0)^2+(x_1-x_0)^2}$$ for $PQ$ $$PQ=\sqrt{(7-5)^2+(4-(-2))^2}=\sqrt{40}=2\sqrt{10}$$