The length of a rectangle is 2 units more than the width. The area of the rectangle is 24 square units. What is the width, in units, of the rectangle?
Question
The length of a rectangle is 2 units more than the width. The area of the rectangle is 24 square units. What is the width, in units, of the rectangle?
Solution
To solve this problem, we can use the formula for the area of a rectangle, which is length times width.
Step 1: Let's denote the width of the rectangle as x (in units).
Step 2: According to the problem, the length of the rectangle is 2 units more than the width. So, we can express the length as x + 2.
Step 3: The area of the rectangle is given as 24 square units. So, we can set up the equation: x * (x + 2) = 24.
Step 4: This equation simplifies to x^2 + 2x - 24 = 0.
Step 5: We can solve this quadratic equation by factoring: (x - 4)(x + 6) = 0.
Step 6: Setting each factor equal to zero gives the solutions x = 4 and x = -6.
Step 7: Since the width of a rectangle cannot be negative, we discard x = -6.
Therefore, the width of the rectangle is 4 units.
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