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.
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