Question

A rectangle has a perimeter of 48 inches. The length of the rectangle is 4 inches shorter than 3 times its width. The equation below shows the perimeter of the rectangle in terms of x, the rectangle's width. 2 (x) + 2(3x − 4) = 48 What does (3x − 4) represent in the equation?

Answer 1

In the equation 2(x) + 2(3x − 4) = 48, (3x − 4) represents the length of the rectangle.

Step-by-step explanation:

Let's analyze the given equation and break it down step by step. The equation represents the perimeter of a rectangle, which is the sum of the lengths of all four sides. The equation is written as 2(x) + 2(3x − 4) = 48.

The term 2(x) corresponds to the width of the rectangle (since the width is typically denoted by x). The expression 3x − 4 represents the length of the rectangle. The equation multiplies the width by 2 and the length by 2 and sets the sum equal to the given perimeter of 48 inches.

So, the term (3x − 4) in the equation specifically represents the length of the rectangle. It is stated in the problem that the length of the rectangle is 4 inches shorter than 3 times its width, which is precisely captured by the expression (3x − 4). Therefore, (3x − 4) corresponds to the length of the rectangle in the given equation.