Math Problem Statement
Solution
We are tasked with finding the width of a rectangle where the length is four times the width, and the area of the rectangle is 1024 cm².
Let's define the variables:
- Let the width of the rectangle be cm.
- Since the length is four times the width, the length of the rectangle will be cm.
- The area of a rectangle is given by the formula:
Substituting the given values:
Solving for :
- Divide both sides by 4:
- Take the square root of both sides:
Thus, the width of the rectangle is 16 cm.
Would you like further details or clarifications?
Here are five related questions to deepen your understanding:
- How would you calculate the length of the rectangle now that you know the width?
- If the area was doubled, what would be the new width?
- What would happen to the width if the length was only three times the width?
- How do you find the perimeter of the rectangle given the width and length?
- Can the area of a rectangle ever be negative? Why or why not?
Tip: Always double-check your equation setup based on the problem conditions to avoid mistakes when solving geometric problems.
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Math Problem Analysis
Mathematical Concepts
Algebra
Geometry
Quadratic Equations
Formulas
Area of a rectangle = length × width
Quadratic equation: ax² = c
Theorems
Properties of Quadratic Equations
Basic Geometry Theorems
Suitable Grade Level
Grades 6-8
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