Question

find the diagonal of a rectangular prism box that has a measure of 3x4x10cm round to nearest tenthh

Answer 1

To find the diagonal of a rectangular prism (also known as a rectangular box), you can use the formula:

\[
d = \sqrt{l^2 + w^2 + h^2}
\]

where \( l \), \( w \), and \( h \) are the lengths of the sides of the prism.

Given the dimensions:

- Length \( l = 3 \) cm
- Width \( w = 4 \) cm
- Height \( h = 10 \) cm

Now, plug in the values:

\[
d = \sqrt{3^2 + 4^2 + 10^2}
\]
\[
d = \sqrt{9 + 16 + 100}
\]
\[
d = \sqrt{125}
\]
\[
d \approx 11.1803
\]

Rounding to the nearest tenth:

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

So, the diagonal of the rectangular prism is approximately **11.2 cm**.