Question

A square and rectangle are shown below. The width of the rectangle is the same as the length of a side of the square, both represented by x. The length of the rectangle is one foot more than twice its width. The perimeter of the rectangle is 26 feet more than that of the square. What is the length of the rectangle?

1) 2x + 1
2) 2x - 1
3) 2x + 2
4) 2x - 2

Answer 1

The length of the rectangle is 9 feet, which corresponds to option 1) 2x + 1.

Step-by-step explanation:

To find the length of the rectangle, we need to set up an equation using the given information. Let the width of the rectangle be x. The length of the rectangle is one foot more than twice its width, so it can be written as 2x + 1. The perimeter of the rectangle is 26 feet more than that of the square, so we can set up the equation: 2(2x + 1) + 2x = 4x + 2 + 2x = 26. Solving this equation, we get 6x + 2 = 26, and then 6x = 24, and finally x = 4 feet. Therefore, the length of the rectangle is 2(4) + 1 = 9 feet. So, the correct answer is option 1) 2x + 1.