a rectangle with a length of 32 units and a width of 18 units; find the length of a diagonal.

To find the length of the diagonal of a rectangle, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the other two sides.

In this case, the length and width of the rectangle form the two sides of a right triangle. Let's label the length as "a" and the width as "b".

Using the Pythagorean theorem, we can write the equation as:

a^2 + b^2 = c^2

where "c" represents the length of the diagonal.

Plugging in the given values, we have:

32^2 + 18^2 = c^2

1024 + 324 = c^2

1348 = c^2

To find the value of "c" (the diagonal length), we need to take the square root of both sides:

sqrt(1348) = sqrt(c^2)

36.74 ≈ c

Therefore, the length of the diagonal of the rectangle is approximately 36.74 units.

a^2 + b^2 = c^2

32^2 + 18^2 = c^2