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A rectangle has a length that is twice its width. If the area of the rectangle i

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Question: A rectangle has a length that is twice its width. If the area of the rectangle is 200 square units, what is the width of the rectangle?

Options:

  1. 10 units
  2. 20 units
  3. 15 units
  4. 25 units

Correct Answer: 10 units

Solution: 

Let the width be x units. Then the length is 2x units. Area = length × width = 2x * x = 2x^2. Setting this equal to 200 gives 2x^2 = 200, so x^2 = 100, and x = 10 units.

A rectangle has a length that is twice its width. If the area of the rectangle i

Practice Questions

Q1
A rectangle has a length that is twice its width. If the area of the rectangle is 200 square units, what is the width of the rectangle?
  1. 10 units
  2. 20 units
  3. 15 units
  4. 25 units

Questions & Step-by-Step Solutions

A rectangle has a length that is twice its width. If the area of the rectangle is 200 square units, what is the width of the rectangle?
  • Step 1: Let the width of the rectangle be represented by the variable x.
  • Step 2: Since the length is twice the width, we can express the length as 2x.
  • Step 3: The formula for the area of a rectangle is Area = length × width.
  • Step 4: Substitute the expressions for length and width into the area formula: Area = 2x * x.
  • Step 5: This simplifies to Area = 2x^2.
  • Step 6: We know the area is 200 square units, so we set up the equation: 2x^2 = 200.
  • Step 7: To solve for x^2, divide both sides of the equation by 2: x^2 = 100.
  • Step 8: To find x, take the square root of both sides: x = 10 units.
  • Area of a Rectangle – Understanding the formula for the area of a rectangle (Area = length × width) and how to manipulate it with given relationships between length and width.
  • Algebraic Manipulation – Solving quadratic equations and understanding how to isolate variables.
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