To find the length of the diagonal of a rectangular painting, you can use the Pythagorean theorem. The formula for the diagonal \( d \) of a rectangle with length \( l \) and width \( w \) is:
\[ d = \sqrt{l^2 + w^2} \]
In this case, the dimensions of the painting are 36 inches (width) and 48 inches (length). Plugging in these values:
\[ d = \sqrt{36^2 + 48^2} \]
Calculating \( 36^2 \) and \( 48^2 \):
\[ 36^2 = 1296 \] \[ 48^2 = 2304 \]
Now add these two results:
\[ d = \sqrt{1296 + 2304} = \sqrt{3600} \]
Finally, calculate the square root:
\[ d = 60 \]
Therefore, the length of the diagonal is 60 inches.
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