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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?

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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.

This problem has been solved

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