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

To find the diagonal of a rectangle we must use the side lengths to create a 90 degree triangle with side lengths of 5, 8, and a hypotenuse which is equal to the diagonal.

If we have a right angle triangle and a value for two of the three side lengths, we use the Pythagorean Theorem to solve for the length of the third side.

The two side lengths that meet to form the right angle are labeled and which are interchangeable for each side length.

The long length connecting them is labeled and is known as the hypotenuse.

The Pythagorean Theorem states

Take 5 and 8 and plug them into the equation as and to yield

First square the numbers

After squaring the numbers add them together

Once you have the sum, square root both sides

After calculating our answer for the diagonal is .

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.