Question

Find the diagonal length of a rectangular painting with dimensions of 36 inches by 48 inches.

Answer 1

To find the diagonal length of a rectangular painting, we can use the Pythagorean theorem. The diagonal \( d \) of a rectangle can be calculated using the formula:

\[
d = \sqrt{width^2 + height^2}
\]

In this case, the dimensions of the painting are:

- Width = 36 inches
- Height = 48 inches

Now, we substitute the values into the formula:

\[
d = \sqrt{36^2 + 48^2}
\]

Calculating \( 36^2 \) and \( 48^2 \):

\[
36^2 = 1296
\]
\[
48^2 = 2304
\]

Now, add these two results:

\[
d = \sqrt{1296 + 2304}
\]
\[
d = \sqrt{3600}
\]

Finally, calculate the square root:

\[
d = 60
\]

Thus, the diagonal length of the painting is \( \boxed{60} \) inches.