Diagonal of Rectangle Formula
Before going to know what is the diagonal of a rectangle formula, let us understand what is meant by the diagonal of a rectangle. The diagonal of a rectangle is a line segment that joins any two of its nonadjacent vertices. In the following rectangle, AC and BD are the diagonals. You can see that the lengths of both AC and BD are the same. Let us learn the diagonal of rectangle formula along with a few solved examples.
What is the Diagonal of Rectangle Formula?
The diagonal of a rectangle formula is derived using Pythagoras theorem. Let us consider a rectangle of length "l" and width "w". Let the length of each diagonal be "d".
Applying Pythagoras theorem to the triangle ABD,
d^{2} = l^{2} + w^{2}
Taking square root on both sides,
d = √( l^{2} + w^{2})
Thus, the diagonal of a rectangle formula is:
d = √( l^{2} + w^{2})
where,
 l = length of the rectangle
 w = width of the rectangle
Let us see the applications of the diagonal of rectangle formula in the following section.

Example 1: Find the length of each diagonal of a rectangle of length 8 units and width 6 units.
Solution:
To find: The length of each diagonal of the given rectangle.
It is given that:
The length of the rectangle, l = 8 units.
The width of the rectangle, w = 6 units.
Using the diagonal of a rectangle formula,
d = √( l^{2} + w^{2})
d = √( 8^{2} + 6^{2})
= √ 100
= 10 units.
Answer: The length of each diagonal = 10 units.

Example 2: The size of the screen of a television is the length of its diagonal. Then find the size of the television whose dimensions are 16 inches and 40 inches.
Solution:
To find: The size (diagonal) of the given television.
It is given that:
The length of the television, l = 40 units.
The width of the television, w = 16 units.
Using the diagonal of a rectangle formula,
d = √( l^{2} + w^{2})
d = √( 40^{2} + 16^{2})
= √ 1856
= 43.08 inches.
Answer: The size (diagonal) of the given television = 43.08 inches.