Question

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.

Answer 1

diagonal from the lowest corner to the upper opposite corner
= `5sqrt(2) ~~ 7.1` cm

Explanation:

Given a rectangular prism: `4 xx 3 xx 5`

First find the diagonal of the base using Pythagorean Theorem:

`b_(diagonal) = 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) ~~ 7.1` cm