Question

I need a little help understanding this

Answer 1

I'm going to use the letters L and W for the length and the width of the granite rectangle. We know that the length is 3 times the width. With this information we can build the following equation:

`3W=L`

We also know that the perimeter of the section must be less than 320 inches. The perimeter of a rectangle is giving by two times its length plus two times its width. Then we have the equations:

`\begin{gathered} \text{Perimeter}=2L+2W \\ \text{Perimeter}<320 \\ 2L+2W<320 \end{gathered}`

Since we know that L=3W then:

`\begin{gathered} L=3W \\ W=(L)/(3) \end{gathered}`

Now that we know that W=L/3 we can substitute L/3 in place of W on the inequality I wrote before:

`\begin{gathered} 2L+2W<320 \\ 2L+2\cdot(L)/(3)<320 \\ (8)/(3)L<320 \\ L<320\cdot(3)/(8) \\ L<120 \end{gathered}`

This means that the length must be less than 120 inches. This is the same as statement D which is the answer for this problem.