The formula for the perimeter of a rectangle is Pequals=2Lplus+​2W, where L is the length of the rectangle and W is the width. You are given the perimeter and the width of a rectangle and you wish to solve for length. Which of the following formulas is the correct solution for the length of the​ rectangle?

Given the formula for the perimeter of a rectangle:

\[
P = 2L + 2W
\]

where:
- \( P \) is the perimeter,
- \( L \) is the length, and
- \( W \) is the width.

You are tasked with solving for the length \( L \).

### Steps:
1. Start with the formula for the perimeter:
   \[
   P = 2L + 2W
   \]
2. Subtract \( 2W \) from both sides:
   \[
   P - 2W = 2L
   \]
3. Divide both sides by 2 to isolate \( L \):
   \[
   L = \frac{P - 2W}{2}
   \]

Thus, the correct formula for the length \( L \) of the rectangle is:

\[
L = \frac{P - 2W}{2}
\]

This formula allows you to compute the length when the perimeter \( P \) and the width \( W \) are known.

Do you have any questions or want more details?

Here are some related questions:
1. How do you derive the formula for the width if the length and perimeter are known?
2. Can this formula be applied to irregular quadrilaterals?
3. How would this formula change if only the area and one dimension are known?
4. What happens to the formula when the rectangle is a square?
5. How can you calculate the diagonal of the rectangle if the perimeter and width are known?

**Tip:** Always check that the calculated values for length and width make sense in the context of the given perimeter!

The formula for the perimeter of a rectangle is P = 2L + 2W, where L is the length of the rectangle and W is the width. You are given the perimeter and the width of a rectangle and you wish to solve for length. Which of the following formulas is the correct solution for the length of the rectangle?

Learn how to find the length of a rectangle using the formula L = (P - 2W) / 2 when the perimeter and width are known. This problem covers key geometric and algebraic concepts, suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation