A pencil box, in the shape of a rectangular prism, measures 15 cm by 20 cm by 8 cm. Find the length of the longest peneil that would fit inside the box,

To find the length of the longest pencil that would fit inside the rectangular prism (pencil box), we need to find the **space diagonal** of the box. The space diagonal is the longest possible straight line that can be drawn inside a rectangular prism.

For a rectangular prism with dimensions \( l \), \( w \), and \( h \), the formula for the space diagonal \( d \) is:

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

Given the dimensions of the pencil box:
- Length (\( l \)) = 15 cm
- Width (\( w \)) = 20 cm
- Height (\( h \)) = 8 cm

Substitute these values into the formula:

\[
d = \sqrt{15^2 + 20^2 + 8^2}
\]

\[
d = \sqrt{225 + 400

A pencil box, in the shape of a rectangular prism, measures 15 cm by 20 cm by 8 cm. Find the length of the longest pencil that would fit inside the box.

Learn how to calculate the length of the longest pencil that can fit inside a rectangular prism-shaped pencil box. This problem applies geometric concepts such as the space diagonal formula and the Pythagorean Theorem, using dimensions of 15 cm, 20 cm, and 8 cm. Suitable for students in Grades 8-10.

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