Question

Find the length and the width of the given rectangle if the perimeter is 104 inches._ 7y + 6 47-9 Response:

Answer 1

The perimeter of a rectangle is given by the formula:

`P=2l+2w`

Where l is the length of the rectangle and w is its width. For this rectangle we know two expressions, one of the length and the other for the width:

`\begin{gathered} l=7y+6 \\ w=4y-9 \end{gathered}`

If we substitute these equations into the formula of the perimeter, we get:

`P=2*(7y+6)+2*(4y-9)`

Simplifying we get:

`\begin{gathered} P=2*(7y+6)+2*(4y-9) \\ P=14y+12+8y-18 \\ P=22y-6 \end{gathered}`

replacing the value of the perimeter (104) and then solving for y we get:

`\begin{gathered} 104=22y-6 \\ 110=22y \\ y=(110)/(22)=5 \end{gathered}`

Now that we know that y equals 5, let's replace it into the formulas of the length and width:

`\begin{gathered} l=7*5+6=41 \\ w=4*5-9=11 \end{gathered}`

Then, the length equals 41 inches and the width equals 11 inches