Question

The length and width of a rectangle are consecutive odd integers. The area of the rectangle is 255 square inches. Find the length and width of

the rectangle.

Width =

Answer 1

The length and width of a rectangle are consecutive odd integers. By using the formula for calculating the area of a rectangle and solving a quadratic equation, we can find the width of the rectangle. The width of the rectangle is 15 inches

Step-by-step explanation:

The length and width of a rectangle are consecutive odd integers. Let's assume the width of the rectangle is 'w' inches. Since the length and width are consecutive odd integers, the length can be represented as 'w + 2'. The area of a rectangle is given by the formula A = length * width. So, we can write the equation: (w + 2) * w = 255. By solving this equation, we can find the value of 'w' which represents the width of the rectangle.

Now, let's solve the equation:

1. Expand the equation: w^2 + 2w = 255
2. Rearrange the equation: w^2 + 2w - 255 = 0
3. Factor the quadratic equation: (w + 17)(w - 15) = 0
4. Set each factor equal to zero and solve for 'w': w + 17 = 0 or w - 15 = 0
5. So, the possible values for 'w' are -17 or 15. However, since the width cannot be negative, the width of the rectangle is 15 inches.

Therefore, the width of the rectangle is 15 inches.