The length of a rectangle is 3 units greater than its width. Which expression would correctly represent the perimeter of the rectangle?
A.
2W+2[W+3]
B.
W+W+3
C.
W[W+3]
D.
2W+2[3W]
The Correct answer and Explanation is:
To find the correct expression representing the perimeter of the rectangle, we first need to understand the relationship between the length and width of the rectangle.
Let’s denote the width of the rectangle as WWW. According to the problem, the length LLL of the rectangle is 3 units greater than its width. Therefore, we can express the length as:L=W+3L = W + 3L=W+3
The formula for the perimeter PPP of a rectangle is given by:P=2L+2WP = 2L + 2WP=2L+2W
Substituting the expression for LLL into the perimeter formula, we get:P=2(W+3)+2WP = 2(W + 3) + 2WP=2(W+3)+2W
Now, we can simplify this expression step by step:
- Distribute 222 in the first term:P=2W+6+2WP = 2W + 6 + 2WP=2W+6+2W
- Combine like terms:P=4W+6P = 4W + 6P=4W+6
Now, let’s analyze the answer choices provided:
A. 2W+2[W+3]2W + 2[W + 3]2W+2[W+3]
This simplifies as follows:2W+2W+6=4W+6(Correct)2W + 2W + 6 = 4W + 6 \quad \text{(Correct)}2W+2W+6=4W+6(Correct)
B. W+W+3W + W + 3W+W+3
This simplifies to:2W+3(Incorrect)2W + 3 \quad \text{(Incorrect)}2W+3(Incorrect)
C. W[W+3]W[W + 3]W[W+3]
This represents the area of the rectangle, not the perimeter, and simplifies to:W2+3W(Incorrect)W^2 + 3W \quad \text{(Incorrect)}W2+3W(Incorrect)
D. 2W+2[3W]2W + 2[3W]2W+2[3W]
This simplifies to:2W+6W=8W(Incorrect)2W + 6W = 8W \quad \text{(Incorrect)}2W+6W=8W(Incorrect)
Thus, the correct expression that represents the perimeter of the rectangle is:A. 2W+2[W+3]\boxed{A. \, 2W + 2[W + 3]}A.2W+2[W+3]
In conclusion, when calculating the perimeter of a rectangle, it’s essential to understand the relationships between the dimensions and to apply the perimeter formula correctly. The other choices do not accurately represent the perimeter based on the conditions given in the problem.