The width of a rectangle is s. Its length is 3s. How long is a diagonal of the rectangle? Express your answer in simplified radical form.

By the pythagorean theorem:

h^2=x^2+y^2, h is the diagonal, and x and y are the sides so ...

d^2=s^2 + (3s) ^2

d^2=s^2+9s^2

d^2=10s^2

d=s√10 (since 10=2*5 neither of which is a square so √10 cannot be simplified any further)

The diagonal is s√10 units