I was given this interesting problem:
The length of a rectangle is 6 feet longer than its width. The perimeter is less than 48 feet. Write a mathematical expression for the width of the rectangle.
How do I go about doing this?
What does the problem say:
Perimeter is less than 48ft.
Let P=perimeter
Let L=length
Let W=width
P<48ft
Express perimeter in terms of length and width:
P=L+W+L+W
or
L+W+L+W<48ft
Express the width as a funtion of L.
Substitute that value into the above equation and solve for W.
Sorry the next to last line should say to express LENGTH as a function of W.
Then, solve for W.
To find the mathematical expression for the width of the rectangle, we need to understand the problem and break it down step by step.
Let's start by considering the given information:
- The length of the rectangle is 6 feet longer than its width.
- The perimeter of the rectangle is less than 48 feet.
Let's assign a variable to represent the width of the rectangle. We can use the letter 'w' to represent the width.
Since the length is 6 feet longer than the width, we can express the length as 'w + 6'.
Now, let's write the algebraic expression for the perimeter of the rectangle. Perimeter is the sum of all the sides of a shape.
The perimeter of a rectangle can be found by adding the lengths of all four sides:
Perimeter = 2(width) + 2(length)
In this case, the width is 'w' and the length is 'w + 6'. So the expression for the perimeter would be:
Perimeter = 2w + 2(w + 6)
We are given that the perimeter is less than 48 feet, so we can set up the inequality:
2w + 2(w + 6) < 48
Now you can solve this inequality to find the range of possible values for the width of the rectangle.