Question

Consecutive Integer Problems - Linear (Level 2)

Score: 3/5 Penalty: none
Question
The perimeter of a rectangle is 40 inches. Find the length and width if
length is an integer and the width is 2 times the next consecutive integ-
Answer Attempt 1 out of 3
Length
=
linches
Show Examp
Width

Answer 1

To find the length and width of a rectangle, we can set up a system of equations. The length is an integer, and the width is 2 times the next consecutive integer. By solving the equations, we find that the length is 5 inches and the width is 12 inches.

Step-by-step explanation:

To find the length and width of the rectangle, we can set up a system of equations based on the given information. Let's say the length is represented by x. The width, which is 2 times the next consecutive integer, can be represented as 2(x+1).

The perimeter of a rectangle is calculated by adding up all the sides. In this case, it is given as 40 inches. So, the equation becomes: 2(x + 2(x+1)) = 40.

Simplifying the equation gives us: 2x + 4x + 8 = 40. Combining like terms gives 6x + 8 = 40. Subtracting 8 from both sides gives 6x = 32. Dividing both sides by 6 gives x = 5.33. However, since the length is an integer, it must be 5. Therefore, the length of the rectangle is 5 inches and the width is 2 times the next consecutive integer, which is 2(5+1) = 12 inches.

Learn more about Consecutive Integer Problems