A rectangular area is to be fenced in along a straight river bank as illustrated. The length of the​ fenced-in area is to be 3 feet greater than the​ width, and the total amount of fencing to be used is 63 feet. Find the width and length of the​ fenced-in area. The width of the​ fenced-in area is Type an integer or a​ fraction

We are given that a rectangular area is to be fenced in along a straight river bank, with the following conditions:

1. The length of the fenced-in area is 3 feet greater than the width.
2. The total amount of fencing to be used is 63 feet.
3. Since one side is along the river bank, only three sides of the rectangle will be fenced: two widths and one length.

Let:
- \( w \) be the width of the fenced-in area.
- \( l \) be the length of the fenced-in area.

From the problem, we know:
1. \( l = w + 3 \) (the length is 3 feet greater than the width).
2. The total amount of fencing is \( 2w + l = 63 \) (since two widths and one length are being fenced).

### Step 1: Set up the equation
Substitute the expression for \( l \) (which is \( l = w + 3 \)) into the fencing equation:

\[
2w + (w + 3) = 63
\]

### Step 2: Simplify the equation
Simplify the equation:

\[
2w + w + 3 = 63
\]
\[
3w + 3 = 63
\]
\[
3w = 60
\]
\[
w = 20
\]

### Step 3: Find the length
Since \( l = w + 3 \), substitute \( w = 20 \) into this equation:

\[
l = 20 + 3 = 23
\]

### Final Answer:
- The width of the fenced-in area is \( 20 \) feet.
- The length of the fenced-in area is \( 23 \) feet.

Would you like more details or have any further questions?

Here are 5 related questions to expand your understanding:
1. What if the total amount of fencing were 80 feet? How would you solve for the new dimensions?
2. How does the formula for the perimeter of a rectangle change if all four sides are fenced?
3. What if the length were 5 feet greater than the width instead of 3 feet?
4. How do you find the area of the fenced-in region?
5. What is the relationship between the width and length if both had to be equal?

**Tip:** Always check the conditions given in the problem to properly set up the equations!

A rectangular area is to be fenced in along a straight river bank as illustrated. The length of the fenced-in area is to be 3 feet greater than the width, and the total amount of fencing to be used is 63 feet. Find the width and length of the fenced-in area.

Learn how to find the width and length of a rectangular area fenced along a river bank with a total fencing of 63 feet. This problem explores key algebraic concepts and linear equations, 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