Chapter 8, Problem 5MCQ

To determine

The possible whole number dimension for the length and the width of the room.

Answer to Problem 5MCQ

The possible dimension of the length and width are:

  $1,2,3,,4,5,6,8,10,12,15,20,24,30,40,60,120$

Explanation of Solution

Given:

The area of the rectangular room is 120 square feet.

The area of the rectangular field is given as:

  $\begin{array}{l}\text{Area=lenngth}\times \text{width}\\ \text{120=lenngth}\times \text{width}\end{array}$

For the possible value of the dimensions, the factors should be determined for the number 120.

The factors of the 120 are:

  $120=1,2,3,,4,5,6,8,10,12,15,20,24,30,40,60,120$

Now, making the combination of the above number in a way that their products are 120:

  $\begin{array}{l}1\times 120\\ 2\times 60\\ 3\times 40\\ 4\times 30\\ 5\times 24\\ 6\times 20\\ 8\times 15\\ 10\times 12\end{array}$

Therefore, from the above factors result, the possible dimension of the length and width are:

  $1,2,3,,4,5,6,8,10,12,15,20,24,30,40,60,120$