Question

Find the diagonal of a rectangular prism box that has measures of 3 x 4 x 10 cm. Round to nearest tenth.

Answer 1

To find the diagonal \( d \) of a rectangular prism (also known as a box) with dimensions \( a \), \( b \), and \( c \), we use the formula:

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

In this case, the dimensions of the box are:

- \( a = 3 \) cm
- \( b = 4 \) cm
- \( c = 10 \) cm

Now, we substitute these values into the formula:

\[
d = \sqrt{3^2 + 4^2 + 10^2}
\]

Calculating each term:

\[
3^2 = 9
\]
\[
4^2 = 16
\]
\[
10^2 = 100
\]

Now, add these values together:

\[
d = \sqrt{9 + 16 + 100} = \sqrt{125}
\]

Next, we calculate \( \sqrt{125} \):

\[
\sqrt{125} = \sqrt{25 \times 5} = 5\sqrt{5}
\]

Using a calculator, \( \sqrt{5} \) is approximately \( 2.236 \), so:

\[
d \approx 5 \times 2.236 \approx 11.18
\]

Rounding to the nearest tenth:

\[
d \approx 11.2 \text{ cm}
\]

Thus, the diagonal of the rectangular prism box is approximately \( \boxed{11.2} \) cm.