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?
Practice Questions
1 question
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?
10 units
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15 units
25 units
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.
Questions & Step-by-step Solutions
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Q
Q: 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?
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.
Steps: 8
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.
