A new 

Community Wellness ComplexCommunity Wellness Complex 

is being built in 

AlstonAlston. 

 The perimeter of the rectangular playing field is 

522522 

yards.  The length of the field is 

44 

yards less than 

quadruplequadruple 

the width.  What are the dimensions of the playing​ field?

We are given the following information:

- The perimeter of the rectangular playing field is \( 522 \) yards.
- The length of the field is \( 44 \) yards less than quadruple the width.

Let:
- \( w \) be the width of the field.
- \( l \) be the length of the field.

### Step 1: Set up the relationships

- The perimeter of a rectangle is given by the formula:
  \[
  P = 2l + 2w
  \]
  Substituting the given perimeter:
  \[
  522 = 2l + 2w
  \]

- We are also told that the length is \( 44 \) yards less than quadruple the width:
  \[
  l = 4w - 44
  \]

### Step 2: Substitute the expression for \( l \)

Now substitute the expression for \( l \) into the perimeter equation:
\[
522 = 2(4w - 44) + 2w
\]

### Step 3: Solve for \( w \)

Expand and simplify the equation:
\[
522 = 8w - 88 + 2w
\]
\[
522 = 10w - 88
\]
Add \( 88 \) to both sides:
\[
610 = 10w
\]
Now, divide both sides by \( 10 \):
\[
w = 61 \text{ yards}
\]

### Step 4: Find the length \( l \)

Using the expression for \( l \):
\[
l = 4w - 44 = 4(61) - 44 = 244 - 44 = 200 \text{ yards}
\]

### Final Dimensions

- Width: \( 61 \) yards
- Length: \( 200 \) yards

Would you like more details on the steps, or do you have any questions?

Here are five related questions to think about:
1. How would the perimeter change if the width increased by 10 yards?
2. If the length was reduced by 10%, how would that affect the dimensions?
3. What is the area of the playing field given the dimensions?
4. How would the dimensions change if the perimeter increased to 600 yards?
5. How would the relationship between length and width change if the length was \( 50 \) yards less than quadruple the width?

**Tip**: When solving word problems, translate the conditions step-by-step into mathematical expressions before attempting to solve.

Discover how to calculate the dimensions of a rectangular playing field for the Community Wellness Complex in Alston. Solve for width and length using perimeter and algebraic equations. Suitable for Grades 7-9 students.

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