The diagonal of a rectangle is also the hypotenuse of a right triangle that has the length and the width of the rectangle as its legs.

We can then use the Pythgorean Theorem to find the diagonal.

For the given rectangle,

A diagonal of a rectangle cuts the rectangle into 2 right triangles with sides equal to the sides of the rectangle and with a hypotenuse that is the diagonal. All you need to do is use the pythagorean theorem:

where a and b are the sides of the rectangle and c is the length of the diagonal.

You should notice that the diagonal of the rectangle is the same as the diameter of the circle.

Now, recall how to find the circumference of a circle.

Since we are given the circumference and need the diameter, rerwite the equation to solve for the diameter.

Plug in the given circumference to find the diameter.

Now, recall the relationship between the diameter of the circle and the diagonal of the rectangle:

The diagonal of a rectangle forms the hypotenuse of a right triangle with one long and one short side of the rectangle. Therefore, to find the diagonal, we use the Pythagorean Theorem using the two side lengths and solving for the hypotenuse:

Then, all we have to do is simplify the radical, as follows:

Therefore, .

You should notice that the diagonal of the rectangle is the same as the diameter of the circle.

Now, recall how to find the circumference of a circle.

Since we are given the circumference and need the diameter, rerwite the equation to solve for the diameter.

Plug in the given circumference to find the diameter.

Now, recall the relationship between the diameter of the circle and the diagonal of the rectangle:

To find the diagonal of a rectangle recall that the diagonal will create a triangle where the width and length are legs of the triangle and the diagonal is the hypotenuse.

To solve, simple use the Pythagorean Theorem and solve for the hypotenuse, which will be the diagonal of the rectangle.

Thus,

The diagonal of a rectangle is also the hypotenuse of a right triangle that has the length and the width of the rectangle as its legs.

We can then use the Pythgorean Theorem to find the diagonal.

For the given rectangle,

If the width is and the length is twice the width, we can calculate the area as such:

1. Use Pythagorean Theorem with and .

2. Solve for , the length of the diagonal:

This rounds down to because the hundredth's place () is less than .

To find the diagonal we use the Pythagorean Theorem:

where = hypotenuse

or