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A rectangle has a length that is 3 times its width. If the perimeter of the rect

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Question: A rectangle has a length that is 3 times its width. If the perimeter of the rectangle is 48 cm, what is the width?

Options:

  1. 4 cm
  2. 6 cm
  3. 8 cm
  4. 10 cm

Correct Answer: 6 cm

Solution: 

Let the width be w cm. Then the length is 3w cm. The perimeter is given by: 2(length + width) = 48. Thus, 2(3w + w) = 48. Simplifying gives 8w = 48, so w = 6 cm.

A rectangle has a length that is 3 times its width. If the perimeter of the rect

Practice Questions

Q1
A rectangle has a length that is 3 times its width. If the perimeter of the rectangle is 48 cm, what is the width?
  1. 4 cm
  2. 6 cm
  3. 8 cm
  4. 10 cm

Questions & Step-by-Step Solutions

A rectangle has a length that is 3 times its width. If the perimeter of the rectangle is 48 cm, what is the width?
  • Step 1: Let the width of the rectangle be represented as 'w' cm.
  • Step 2: Since the length is 3 times the width, we can express the length as '3w' cm.
  • Step 3: The formula for the perimeter of a rectangle is: Perimeter = 2(length + width).
  • Step 4: Substitute the expressions for length and width into the perimeter formula: 2(3w + w) = 48.
  • Step 5: Simplify the equation inside the parentheses: 3w + w = 4w, so we have 2(4w) = 48.
  • Step 6: Now simplify the equation: 8w = 48.
  • Step 7: To find 'w', divide both sides of the equation by 8: w = 48 / 8.
  • Step 8: Calculate the value: w = 6 cm.
  • Algebraic Expressions – Understanding how to express relationships between variables, such as length and width in this case.
  • Perimeter of a Rectangle – Applying the formula for the perimeter of a rectangle to solve for unknown dimensions.
  • Linear Equations – Solving linear equations to find the value of a variable.
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