# Using Pythagorean Theorem, if you have a box that is 4cm wide, 3cm deep, and 5cm high, what is the length of the longest segment that will fit in the box? Please show working.

May 7, 2018

diagonal from the lowest corner to the upper opposite corner
= $5 \sqrt{2} \approx 7.1$ cm

#### Explanation:

Given a rectangular prism: $4 \times 3 \times 5$

First find the diagonal of the base using Pythagorean Theorem:

${b}_{\mathrm{di} a g o n a l} = \sqrt{{3}^{2} + {4}^{2}} = \sqrt{25} = 5$ cm

The $h = 5$ cm

diagonal of prism $\sqrt{{5}^{2} + {5}^{2}} = \sqrt{50} = \sqrt{2} \sqrt{25} = 5 \sqrt{2} \approx 7.1$ cm