
The perimeter of a rectangle is 148 feet. The length is 14 feet less than 4 times the width.
What are the dimensions of the​ rectangle?

We can solve this problem step by step by using the given information and creating equations.

### Given:
1. The perimeter of the rectangle is 148 feet.
2. The length is 14 feet less than 4 times the width.

### Let:
- \( L \) = length of the rectangle
- \( W \) = width of the rectangle

### Step 1: Perimeter formula
The formula for the perimeter of a rectangle is:

\[
P = 2L + 2W
\]

Given that \( P = 148 \), we can set up the equation:

\[
2L + 2W = 148
\]

### Step 2: Express the length in terms of the width
From the problem, we know that the length is 14 feet less than 4 times the width. So, we can express \( L \) as:

\[
L = 4W - 14
\]

### Step 3: Substitute the expression for \( L \) into the perimeter equation
Now substitute \( L = 4W - 14 \) into the perimeter equation:

\[
2(4W - 14) + 2W = 148
\]

### Step 4: Simplify the equation
First, expand the terms:

\[
8W - 28 + 2W = 148
\]

Combine like terms:

\[
10W - 28 = 148
\]

### Step 5: Solve for \( W \)
Add 28 to both sides:

\[
10W = 176
\]

Now, divide both sides by 10:

\[
W = 17.6
\]

### Step 6: Find \( L \)
Now that we have \( W = 17.6 \), substitute it into the expression for \( L \):

\[
L = 4(17.6) - 14 = 70.4 - 14 = 56.4
\]

### Final Dimensions:
- Width \( W = 17.6 \) feet
- Length \( L = 56.4 \) feet

Would you like further details or clarifications?

---

Here are 5 related questions to expand on this problem:

1. How do you find the area of the rectangle with these dimensions?
2. What would happen if the perimeter was doubled but the relationship between length and width stayed the same?
3. How can this type of problem be solved graphically?
4. Can you create a similar problem involving a square instead of a rectangle?
5. How would the problem change if the perimeter was given in meters instead of feet?

**Tip:** Always check the units of measurements (feet, meters, etc.) in geometry problems to ensure consistency.

The perimeter of a rectangle is 148 feet. The length is 14 feet less than 4 times the width. What are the dimensions of the​ rectangle?

Solve the problem of finding the dimensions of a rectangle with a perimeter of 148 feet, where the length is 14 feet less than 4 times the width. Step-by-step algebraic and geometric solution 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