Chapter 10.1, Problem 14P

How long is the diagonal of a 12 mm-by-16 mm face of a rectangular prism?

To determine

To find the length of the diagonal.

Answer to Problem 14P

The length of the diagonal is $20$ mm.

Explanation of Solution

Given information:

The given statement is:

“How long is the diagonal of $12$ mm by $16$ mm face of a rectangular prism?”

Formula used:

The following formula is used:

  ${\left(hypotenuse\right)}^2={\left(base\right)}^2+{\left(height\right)}^2$

Calculation:

The solution can be obtained by:

  $\begin{array}{l}{\left(diagonal\right)}^2={\left(length\right)}^2+{\left(width\right)}^2\left[\text{Pythagoras theorem}\right]\\ {\left(diagonal\right)}^2={16}^2+{12}^2\left[\text{Substitute the values}\right]\\ {\left(diagonal\right)}^2=256+144\\ diagonal=\sqrt{400}\left[\text{Square root of both sides}\right]\\ diagonal=20\end{array}$

Hence, the length of the diagonal is $20$ mm.