Playgrounds

(1) 50

(2) 150

Explanation

Analyze

• The perimeter is 400 ft. (Given)
• The length is three times as long as the width. (Given)
• What is the length and what is the width of the rectangle? (Find)

Form

We will let w = the width of the playground. There is a second unknown quantity: the length of the playground. We look for a key phrase to help us decide how to represent it using an algebraic expression.

Key phrase: length three times the width

Translation: multiply width by 3

So 3w = the length of the playground.

The formula for the perimeter of a rectangle is P = 2l + 2w.  In words, we can write

• 2 · (the length of the playground) plus 2 · (the width of the playground) is (the perimeter)
• 2 · 3w + 2 · w = 400

Solve

• We need to isolate w on the left side
  • 2 · 3w + 2w = 400
• Do the multiplication: 2 · 3w = 6w
  • 6w + 2w = 400
• On the left side, combine like terms: 6w + 2w = 8w
  • 8w = 400
• To isolate w, divide both sides by 8 to undo the multiplication by 8.
  • \(\frac{8w}{8} = \frac{400}{8}\)
• Do the division
  • w = 50

To find the second unknown, we substitute 50 for w in the expression that represents the length of the playground

• Substitute 50 for w
  • 3w = 3(50)
• This is the length of the playground
  • = 150

State

The width of the playground is 50 feet and the length is 150 feet

Check

If we add two lengths and two widths, we get 2(150) + 2(50) = 300 + 100 = 400.  Also, the length (150 ft) is three times the width (50 ft).  The results checks.