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A rectangle has a length that is twice its width. If the perimeter of the rectan

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

Options:

  1. 96 cm²
  2. 144 cm²
  3. 192 cm²
  4. 48 cm²

Correct Answer: 144 cm²

Solution: 

Let the width be x cm, then the length is 2x cm. The perimeter is given by 2(length + width) = 48, which simplifies to 2(2x + x) = 48, leading to x = 8 cm. The area is length × width = 2x * x = 2(8)(8) = 128 cm².

A rectangle has a length that is twice its width. If the perimeter of the rectan

Practice Questions

Q1
A rectangle has a length that is twice its width. If the perimeter of the rectangle is 48 cm, what is the area of the rectangle?
  1. 96 cm²
  2. 144 cm²
  3. 192 cm²
  4. 48 cm²

Questions & Step-by-Step Solutions

A rectangle has a length that is twice its width. If the perimeter of the rectangle is 48 cm, what is the area of the rectangle?
  • Step 1: Let the width of the rectangle be x cm.
  • Step 2: Since the length is twice the width, the length is 2x cm.
  • Step 3: The formula for the perimeter of a rectangle is 2(length + width).
  • Step 4: Substitute the values for length and width into the perimeter formula: 2(2x + x) = 48.
  • Step 5: Simplify the equation: 2(3x) = 48.
  • Step 6: Divide both sides by 2: 3x = 24.
  • Step 7: Divide both sides by 3 to find x: x = 8 cm (this is the width).
  • Step 8: Now, find the length by substituting x back: length = 2x = 2(8) = 16 cm.
  • Step 9: Calculate the area using the formula: Area = length × width = 16 cm × 8 cm.
  • Step 10: Multiply to find the area: Area = 128 cm².
  • Perimeter and Area of a Rectangle – Understanding the relationship between the length, width, perimeter, and area of a rectangle.
  • Algebraic Manipulation – Using algebra to solve for unknown variables based on given relationships.
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