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Vijay is building a new rectangular enclosure in his backyard for his chickens. He has 40 feet of fencing material and he wants the width of the enclosure to be 8 feet. If l is the length of the enclosure, and Vijay uses all of the fencing material, which equation best models the situation? Choose 1 answer: (A) l+8=40 (B) 2l+8=40 (C) 2(l+8)=40 (D) 2l+2(l+8)=40

Vijay is building a new rectangular enclosure in his backyard for his chickens. He has 4040 feet of fencing material and he wants the width of the enclosure to be 88 feet. If l l is the length of the enclosure, and Vijay uses all of the fencing material, which equation best models the situation?\newlineChoose 11 answer:\newline(A) l+8=40 l+8=40 \newline(B) 2l+8=40 2 l+8=40 \newline(C) 2(l+8)=40 2(l+8)=40 \newline(D) 2l+2(l+8)=40 2 l+2(l+8)=40

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Q. Vijay is building a new rectangular enclosure in his backyard for his chickens. He has 4040 feet of fencing material and he wants the width of the enclosure to be 88 feet. If l l is the length of the enclosure, and Vijay uses all of the fencing material, which equation best models the situation?\newlineChoose 11 answer:\newline(A) l+8=40 l+8=40 \newline(B) 2l+8=40 2 l+8=40 \newline(C) 2(l+8)=40 2(l+8)=40 \newline(D) 2l+2(l+8)=40 2 l+2(l+8)=40
  1. Understand problem and relationship: Understand the problem and the relationship between the length and the perimeter of the enclosure.\newlineVijay is building a rectangular enclosure with a fixed amount of fencing material, which is 4040 feet. The perimeter of a rectangle is given by the formula P=2l+2wP = 2l + 2w, where ll is the length and ww is the width. Since the width is given as 88 feet, we can substitute ww with 88 in the formula to find the relationship involving the length ll.
  2. Substitute given width: Substitute the given width into the perimeter formula.\newlineUsing the formula P=2l+2wP = 2l + 2w and substituting w=8w = 8 feet, we get P=2l+2(8)P = 2l + 2(8). Since the total amount of fencing material is 4040 feet, we can set the perimeter equal to 4040 feet.
  3. Write equation with perimeter: Write the equation with the given perimeter.\newlineSubstituting the values into the equation, we get 40=2l+2(8)40 = 2l + 2(8). This equation represents the total amount of fencing material used for the enclosure.
  4. Simplify the equation: Simplify the equation.\newlineSimplifying the equation, we get 40=2l+1640 = 2l + 16. This equation needs to be further simplified to isolate the variable ll.
  5. Solve for l: Solve for l.\newlineTo solve for l, we need to subtract 1616 from both sides of the equation to isolate the term with ll. Doing so, we get 40−16=2l40 - 16 = 2l, which simplifies to 24=2l24 = 2l. Then, we divide both sides by 22 to find ll. The equation becomes l=24/2l = 24 / 2, which simplifies to l=12l = 12.
  6. Check equation before solving: Check if the equation before solving for ll matches any of the answer choices.\newlineBefore we solved for ll, we had the equation 40=2l+1640 = 2l + 16. This equation can be rewritten as 2(l+8)=402(l + 8) = 40, which matches answer choice (C). Therefore, the correct equation that models the situation is 2(l+8)=402(l + 8) = 40.

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