What is the length of the diagonal in a cuboid with sides 3 cm, 4 cm, and 5 cm?

The length of the diagonal in a cuboid with sides 3 cm, 4 cm, and 5 cm is √50 cm.

To find the length of the diagonal in a cuboid, we use the formula for the space diagonal, which is derived from the Pythagorean theorem. The formula is:

\[ d = \sqrt{a^2 + b^2 + c^2} \]

where \( a \), \( b \), and \( c \) are the lengths of the sides of the cuboid. In this case, the sides are 3 cm, 4 cm, and 5 cm. Plugging these values into the formula, we get:

\[ d = \sqrt{3^2 + 4^2 + 5^2} \]

First, we calculate the squares of each side:

\[ 3^2 = 9 \]
\[ 4^2 = 16 \]
\[ 5^2 = 25 \]

Next, we add these squares together:

\[ 9 + 16 + 25 = 50 \]

Finally, we take the square root of the sum:

\[ d = \sqrt{50} \]

So, the length of the diagonal is √50 cm. If you want to express this as a decimal, √50 is approximately 7.07 cm. This method ensures you accurately find the diagonal length in any cuboid by considering all three dimensions.