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

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?

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.