Question

The perimeter of a toddler play area is $100$feet. The length is ten more than three times the width. Find the length and width of the play area.

Short answer

The length and width of the play area are $40$and $10$ feet respectively.

Step-by-step solution

Given information is,

The perimeter of a toddler play area is $100$feet.

The length is ten more than three times the width.

To find:

The length and width of the play area.

Let us consider,

$l$represents the length of the play area.

$w$represents the width of the play area.

The perimeter of a toddler play area is $100$feet.

From the above lines the obtained equation is,

$$\begin{gathered} 2\left(l+w\right)=100 \\ l+w=50 \end{gathered}$$

The length is ten more than three times the width.

So,$l=10+3w$.

From the step 3,

The obtained linear equations are,

$$\begin{gathered} l+w=50 \\ l=10+3w \end{gathered}$$

Now substitute $l=10+3w$in the equation $l+w=50$.

$$\begin{gathered} 10+3w+w=50 \\ 10+4w=50 \\ 4w=50-10 \\ 4w=40 \\ w=\frac{40}{4} \\ w=10 \end{gathered}$$

Find the value of l.

Now substitute the value of $w$in the equation $l+w=50$.

$$\begin{gathered} l+10=50 \\ l=50-10 \\ l=40 \end{gathered}$$