Question

rectangle expressions – new version
the width of the rectangle is 2x inches and the length is (4x - 3) inches.
1.
carlos represented the perimeter of the rectangle using the expression:
2x+(4x-3)+2x+(4x-3)
explain how carlos’s expression represents the perimeter of the rectangle.

Explanation:

Step1: Recall Perimeter Definition

Perimeter of a rectangle is the sum of all its sides. A rectangle has two equal lengths and two equal widths.

Step2: Identify Sides in Expression

The width is \(2x\) and length is \((4x - 3)\). Carlos's expression is \(2x+(4x - 3)+2x+(4x - 3)\). Here, the first \(2x\) is one width, \((4x - 3)\) is one length, the second \(2x\) is the other width, and the second \((4x - 3)\) is the other length.

Step3: Sum of Sides Gives Perimeter

By adding all four sides (two widths and two lengths) together, we get the total distance around the rectangle, which is the perimeter. So Carlos's expression adds each side (width, length, width, length) to calculate the perimeter.

Answer:

Carlos's expression \(2x+(4x - 3)+2x+(4x - 3)\) represents the perimeter because a rectangle has two sides of width \(2x\) and two sides of length \((4x - 3)\). The perimeter is the sum of all four sides, so adding one width, one length, the other width, and the other length (in that order) gives the total perimeter.