The length of a rectangle

Question

The length of a rectangle is 6 inches more than the width. The perimeter is 48 inches. Find the length and the width of the rectangle.

Answer 1

Hello Paige,

First, let's assign some expressions to form an equation, fair enough?

According to the problem:

w = x <----width is not given in the problem.

l = x + 6 <----length is 6 inches more than the width

We are given the perimeter, which is 48 inches.

The formula or equation for the perimeter of a rectangle is as follows:

P = 2 (l + w) or P = 2 (l) + 2 (w) P equals perimeter, l equals the length, and w equals width in both formulas. Please note: The second formula is simply the result of applying the distributive law in math. I prefer using the second formula.

P = 2 (x + 6) + 2 (x)

P = 2x + 12 + 2x

48 = 4x + 12

36 = 4x

x = 9 <----This is the width of your rectangle.

x + 6 = 15 <-----This is the length of your rectangle.

Now, let's check our work, okay?

P = 2 (15) + 2 (9)

48 = 30 + 18

48 = 48

The solution checks and is verified. I hope this solution assists you and should you have a need for further clarification or want to ask a question regarding the solution or leave feedback, please feel free to do so in the comment section beneath the solution. Should you need further assistance, please feel free to reach out to any of the qualified tutors on this site. Best!