What is the length of the diagonal of a rectangle that is 6 units wide and 8 units long?

To find the length of the diagonal of a rectangle, the Pythagorean theorem is used. The theorem states that in a right triangle, the square of the length of the hypotenuse (which in this case is the diagonal of the rectangle) is equal to the sum of the squares of the lengths of the other two sides.

In this scenario, the width of the rectangle is one side and the length is the other side. The width is given as 6 units and the length is 8 units. According to the Pythagorean theorem:

[

\text{Diagonal}^2 = \text{Width}^2 + \text{Length}^2

]

Substituting the given values:

[

\text{Diagonal}^2 = 6^2 + 8^2

]

[

\text{Diagonal}^2 = 36 + 64

]

[

\text{Diagonal}^2 = 100

]

To find the length of the diagonal, take the square root of both sides:

[

\text{Diagonal} = \sqrt{100} = 10

]

Therefore, the length of the diagonal of the rectangle is