Chapter 6.4, Problem 32PPS

To determine

The length of the metal supports to be cut for the bookshelf to be square.

Answer to Problem 32PPS

  $x=39\text{ inches}$

Explanation of Solution

Given:

Jody is building a bookshelf.

Calculation:

For the bookshelf to be square, all the angles made by shelves and supports are right angles.

A square is also a rectangle. And, according to the definition of rectangle, the two metal supports in the bookshelf will be of same length.

Using the Pythagoras Theorem to find the length of metal supports:

Suppose the length of the metal support be x. And, the width of the rectangle is 15 inches (given).

  $\begin{array}{l}\text{length}=3\text{ feet}\\ \text{length = 36 inches}\end{array}$

Now,

  $\begin{array}{l}x=\sqrt{lengt{h}^2+widt{h}^2}\\ x=\sqrt{{36}^2+{15}^2}\\ x=\sqrt{1521}\\ x=39\text{ inches}\end{array}$