The length and width of the rectangle are in a ratio of 3:4, so the sides can be written as 3_x_ and 4_x_.

We also know the area, so we write an equation and solve for x:

(3_x_)(4_x_) = 12_x_2 = 108.

x2 = 9

x = 3

Now we can recalculate the length and the width:

length = 3x = 3(3) = 9 centimeters

width = 4x = 4(3) = 12 centimeters

Using the Pythagorean Theorem we can find the diagonal, c:

length2 + width2 = c2

92 + 122 = _c_2

81 + 144 = c2

225 = c2

c = 15 centimeters

The diagonal of the rectangle is equivalent to finding the length of the hypotenuse of a right triangle with sides 3 and 4. Using the Pythagorean Theorem:

Therefore the diagonal of the rectangle is 5 feet.