Question

susan plans to use 120 feet of fencing to enclose a rectangular area for a garden. which equation best models the area, y of the rectangular garden that she creates if one side is x feet long? a = lw 〇 y = (60 - x)(x) 〇 y = (120 - x)(120 + x) 〇 y = (120 - x)(x) 〇 y = (60 - x)(60 + x)

Explanation:

Step1: Find perimeter relation

The perimeter of a rectangle is $P=2(l+w)$. Given $P=120$ and one side $l=x$, substitute:
$$120=2(x+w)$$

Step2: Solve for the other side

Divide both sides by 2, then isolate $w$:
$$60=x+w \implies w=60-x$$

Step3: Substitute into area formula

Use area formula $A=lw$, where $A=y$, $l=x$, $w=60-x$:
$$y=x(60-x)$$

Answer:

$y=(60-x)(x)$