Adiagonal of a rectangle measures 9 meters. the width of the rectangle is 6 meters. what is the length of the rectangle?

The diagonal is equal to the hypotenuse of a right triangle having sides of length x and y.  Here we are told that the width is 6 meters and the hypotenuse is 9 meters. So by the Pythagorean Theorem:

h^2=x^2+y^2 so we have:

6^2+L^2=9^2

36+L^2=81

L^2=81-36

L^2=45

L=√45

L=√(3*3*5)

L=3√5 meters