Chapter 10.2, Problem 22P

A pool is shaped like a rectangle with a length 4 times its width w. What is an expression for the distance between opposite corners of the pool?

To determine

To find an expression for the distance between opposite corners of the pool.

Answer to Problem 22P

The distance between opposite corners of the pool can be given by the expression $d=w\sqrt{17}$ .

Explanation of Solution

Given information:

A pool is shaped like a rectangle with a length $4$ times its width $w$ .

Calculation :

The width is $w$ and the length is $4w$ .

Let the distance between the opposite corners of the pool be $d$ .

The expression can be obtained by:

$\begin{array}{l}{d}^2={\left(4w\right)}^2+{\left(w\right)}^2\\ d^2=16w^2+w^2\\ d=\sqrt{17w^2}\\ d=w\sqrt{17}\end{array}$

Hence, the distance between opposite corners of the pool can be given by the expression $d=w\sqrt{17}$ .