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? $\newline$ Choose $1$ answer: $\newline$ (A) $l+8=40$ $\newline$ (B) $2 l+8=40$ $\newline$ (c) $2(l+8)=40$ $\newline$ (D) $2 l+2(l+8)=40$

Full solution

Q. 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?

\newline

Choose

1

answer:

\newline

(A)

l+8=40

\newline

(B)

2 l+8=40

\newline

(c)

2(l+8)=40

\newline

(D)

2 l+2(l+8)=40

Identify Total Fencing Material: Identify the total amount of fencing material and the given width. Calculate the perimeter needed using the formula for the perimeter of a rectangle, $P = 2(\text{length} + \text{width})$ . Here, the total fencing material is $40$ feet, and the width is $8$ feet.
Calculate Perimeter Using Formula: Substitute the known values into the perimeter formula to find the equation for the length. Since the perimeter is $40$ feet and the width is $8$ feet, the equation becomes $2(l + 8) = 40$ .
Substitute Values into Equation: Check if the equation $2(l + 8) = 40$ correctly represents the situation where the total perimeter is used up by the length and twice the width. This equation accounts for both lengths and both widths, matching the problem's conditions.