Question

Adrianne wants to create an outdoor rectangular kennel. The length will be three feet more than twice the width. Write and use an equation to find the length and the width of the kennel if Adrianne has 54 feet of fencing.

Short answer

The length of the kennel is 19 feet and the width is 8 feet.

Step-by-step solution

Step 1. Assign variables for the length and width.

A variable is a letter or a literal used to signify an unknown quantity.

Let letter represent the width of the kennel then as per the question, length of the kennel is 3 feet more than twice the width of the kennel thus,

$Length=2w+3$

Step 2. Form an equation of the perimeter of the kennel.

A rectangular kennel will have a perimeter formed by lengths on two sides and widths on two sides. It is also given that total fencing available is 54 feet thus we have

$2\times Length+2\times width=54$

Next we know that, width is $w$and $Length=2w+3$,we plug these value to get:

$2\left(2w+3\right)+2\times \left(w\right)=54$

Step 3. Simplify the equation.

We obtained the equation $2\left(2w+3\right)+2\times \left(w\right)=54$, to simplify it, we open the brackets as shown:

$\begin{array}{l}2\left(2w+3\right)+2\times \left(w\right)=54\\ 2\times 2w+2\times 3+2w=54\\ 4w+6+2w=54\end{array}$

Like terms are the terms having the same variables and is raised to the same index. A coefficient is the appended number in front of the variable; if no number is shown then we assume it to be 1.

Unlike terms are the terms not having the same variables and or are raised to a different index.

For example, 4 and$5x$ are unlike terms.

We can add like terms by adding their coefficients, we cannot add the unlike terms.

Now we are having the expression $4w+6+2w=54$, combining like terms we get:

$\begin{array}{l}4w+6+2w=54\\ 6w+6=54\end{array}$

Step 4. Solve the equation.

Now we are having the expression $6w+6=54$, subtracting 6 both sides we get:

$\begin{array}{l}6w+6=54\\ 6w+6-6=54-6\\ 6w=48\end{array}$

Dividing b both sides by 6 we get:

$\begin{array}{l}\frac{6w}{6}=\frac{48}{6}\\ w=8\end{array}$

Thus, the width of the kennel is 8 feet.

Step 5. Use a value of width to get the value of length.

We know that $Length=2w+3$and$w=8$ thus we get:

$\begin{array}{l}Length=2\times 8+3\\ Length=19\end{array}$

Thus the Length of the kennel is 19 feet.