Chapter CSB1.2, Problem 30E

a.

To determine

The largest square tile that L can use to cover the table such that she doesn’t have to cut any tiles.

Answer to Problem 30E

6 inches.

Explanation of Solution

Given information:

Length of table = 30 in.

Width of table = 24 in.

Calculation:

The size of largest tile she can use will be equal to GCF of 30 and 24.

Now, prime factors of 30 and 24 are

  $\begin{array}{l}30=2\times 3\times 5\\ 24=2\times 2\times 2\times 3\end{array}$

Therefore GCF of 30 and 24 = $2\times 3=6$

Hence size of largest square tile will be 6 inches.

b.

To determine

The number of tiles needed.

Answer to Problem 30E

20

Explanation of Solution

Given information:

Length of table = 30 in.

Width of table = 24 in.

Calculation:

Number of tiles needed

  $=\frac{\text{Area}\text{of}\text{table}}{\text{Area}\text{of}\text{each}\text{tile}}$

  $=\frac{24\times 30}{6\times 6}$

  $=4\times 5=20$