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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 meters, what is the width of the rectangle?

Options:

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

Correct Answer: 20 meters

Solution: 

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

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 meters, what is the width of the rectangle?
  1. 10 meters
  2. 20 meters
  3. 25 meters
  4. 15 meters

Questions & Step-by-Step Solutions

A rectangle has a length that is twice its width. If the area of the rectangle is 200 square meters, what is the width of the rectangle?
  • Step 1: Let the width of the rectangle be represented as 'x' meters.
  • Step 2: Since the length is twice the width, we can express the length as '2x' meters.
  • 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 meters, 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 = √100.
  • Step 9: Therefore, x = 10 meters, which is the width of the rectangle.
  • 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.
  • Proportional Relationships – Recognizing and applying the relationship between length and width in a rectangle.
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