Question

A rectangle has a length of (x + 2) and a width of (3x - 1). Write an expression in simplest form for the perimeter of the rectangle.

Answer 1

The perimeter of a rectangle with length (x + 2) and width (3x - 1) is calculated as P = 2l + 2w. By substituting the given dimensions and simplifying, the perimeter in simplest form is found to be 8x + 2.

Step-by-step explanation:

The perimeter of a rectangle is calculated by adding the lengths of all four sides. Since a rectangle has two pairs of equal sides, the perimeter formula is P = 2l + 2w, where l is the length and w is the width of the rectangle.

Given the length is (x + 2) and the width is (3x - 1), the expression for the perimeter P is:

P = 2(x + 2) + 2(3x - 1)

To simplify, distribute the 2:

P = 2x + 4 + 6x - 2

Combine like terms:

P = 8x + 2

So the perimeter of the rectangle in simplest form is 8x + 2.