Questions: A rectangle is drawn so that the width is 2 feet shorter than the length. The area of the rectangle is 63 square feet. Find the length of the rectangle.

Solution Steps

To find the length of the rectangle, we can set up an equation using the given information. Let \( L \) be the length of the rectangle. Then the width \( W \) is \( L - 2 \). The area of the rectangle is given by the product of its length and width, which is 63 square feet. We can set up the equation \( L \times (L - 2) = 63 \) and solve for \( L \).

Let \( L \) be the length of the rectangle. The width \( W \) is given by \( L - 2 \). The area of the rectangle is given by the product of its length and width, which is 63 square feet. Therefore, we can set up the equation: \[ L \times (L - 2) = 63 \]

Rewriting the equation, we get: \[ L^2 - 2L - 63 = 0 \] Solving this quadratic equation, we find the solutions: \[ L = 9 \quad \text{or} \quad L = -7 \]

Since the length of a rectangle cannot be negative, we discard \( L = -7 \). Therefore, the length of the rectangle is: \[ L = 9 \]

Final Answer