Question

Set up an equation that can be used to solve the problem. Solve the equation and determine the desired value.

Jim is building a rectangular deck and wants the length to be 1ft greater than the width. What will be the dimensions of the deck if the perimeter is to be 82 A?
The equation is . The width of the deck is
ft and the length ist. (Type an equation using x as the variable.)
O
C

Answer 1

So let's use x for the width of the rectangle and y for its length. We know that the length is 1ft grater than the width. This means that the length is equal to the width plus 1 ft:

`y=x+1`

The perimeter is composed of two lengths and 2 widths which means that the sum of these four sides must be equal to 82:

`82=2x+2y`

We can substitute y with the expression we found before:

`\begin{gathered} 82=2x+2y=2x+2\cdot(x+1) \\ 82=2x+2x+2 \\ 82=4x+2 \end{gathered}`

Know that we have the equation we can find x and y. We can start by substracting 2 from both sides:

`\begin{gathered} 82-2=4x+2-2 \\ 80=4x \end{gathered}`

Then we divide both sides by 4:

`\begin{gathered} (80)/(4)=4x \\ 20=x \end{gathered}`

So the width is 20 ft long. Then the length y is given by:

`\begin{gathered} y=x+1=20+1 \\ y=21 \end{gathered}`

So the length is 21 ft. Then the answers to the boxes in order are:

82=2x+2(x+1)

x=20

y=21