Question

The length of a rectangle is represented by (x^2 + 4x - 5), and the width is represented by (x^2 + 5x + 6). Express the perimeter of the rectangle as a trinomial. Find the area of the rectangle using the box method.

A. Perimeter: 2x^2 + 9x + 1, Area: (x^2 + 4x - 5)(x^2 + 5x + 6)
B. Perimeter: 2x^2 + 9x + 11, Area: (x^2 + 4x - 5)(x^2 + 5x + 6)
C. Perimeter: x^2 + 9x + 1, Area: (x^2 + 4x - 5)(x^2 + 5x + 6)
D. Perimeter: x^2 + 9x + 11, Area: (x^2 + 4x - 5)(x^2 + 5x + 6)

Answer 1

To calculate the perimeter of a rectangle with given dimensions, the formula 2(length + width) is used; for area, the length is multiplied by the width. The perimeter simplifies to 2x^2 + 18x + 2 and the area is a polynomial found using the box method.

Step-by-step explanation:

The provided dimensions of a rectangle are the length (x2 + 4x - 5) and the width (x2 + 5x + 6). To find the perimeter of the rectangle, we use the formula 2(length + width), which gives us 2((x2 + 4x - 5) + (x2 + 5x + 6)), simplifying to 2x2 + 18x + 2.

The area of the rectangle can be found by multiplying the length and width, which is represented by the expression (x2 + 4x - 5)(x2 + 5x + 6). Using the box method, we would multiply each term of the length by each term of the width, summing the products to find the area as a polynomial.