Lance is building a rectangular fence for his chickens. He wants the length to be three times the width and he has 80 feet of fencing. What is the largest possible length? Write an equation and solve.

A. [tex]\(8w = 80\)[/tex]; 30
B. [tex]\(4w = 80\)[/tex]; 15
C. [tex]\(4w = 80\)[/tex]; 20
D. [tex]\(8uq = 80\)[/tex]; 10



Answer :

To solve the problem of finding the largest possible length of the fence, let's follow the structured steps:

1. Define the Variables:
- Let the width of the rectangle be [tex]\( w \)[/tex].
- Since Lance wants the length to be three times the width, the length [tex]\( l \)[/tex] can be defined as [tex]\( l = 3w \)[/tex].

2. Use the Perimeter Constraint:
- The perimeter of a rectangle is calculated using the formula: [tex]\( 2 \times \text{length} + 2 \times \text{width} \)[/tex]
- We're given that the total perimeter is 80 feet.

3. Set Up the Equation:
- Substituting the length and width into the perimeter formula:
[tex]\[ 2l + 2w = 80 \][/tex]
- Replace [tex]\( l \)[/tex] with [tex]\( 3w \)[/tex]:
[tex]\[ 2(3w) + 2w = 80 \][/tex]
- Simplify the equation:
[tex]\[ 6w + 2w = 80 \][/tex]
[tex]\[ 8w = 80 \][/tex]

4. Solve for [tex]\( w \)[/tex]:
- Divide both sides of the equation by 8 to isolate [tex]\( w \)[/tex]:
[tex]\[ w = \frac{80}{8} \][/tex]
[tex]\[ w = 10 \][/tex]

5. Find the Length:
- Recall that the length [tex]\( l \)[/tex] is three times the width:
[tex]\[ l = 3w \][/tex]
- Substitute the value of [tex]\( w \)[/tex] into this equation:
[tex]\[ l = 3 \times 10 \][/tex]
[tex]\[ l = 30 \][/tex]

Therefore, the largest possible length of the fence is [tex]\( \boxed{30} \)[/tex] feet.