susan plans to use 120 feet of fencing to enclose a rectangular area for a garden. which equation best…

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?\n$a = lw$\n$y=(60 - x)(x)$\n$y=(120 - x)(120 + x)$\n$y=(120 - x)(x)$\n$y=(60 - x)(60 + x)$

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?\n$a = lw$\n$y=(60 - x)(x)$\n$y=(120 - x)(120 + x)$\n$y=(120 - x)(x)$\n$y=(60 - x)(60 + x)$

Answer

Answer:

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

Explanation:

Step1: Recall perimeter formula

For a rectangle, $P = 2(l + w)$. Given $P=120$, so $120 = 2(l + w)$.

Step2: Solve for the other - side length

Dividing both sides of $120 = 2(l + w)$ by 2 gives $60=l + w$. If one side is $x$, then the other side is $60 - x$.

Step3: Recall area formula

The area of a rectangle $A=lw$. Here, $y = A$, and substituting the side - lengths we get $y=(60 - x)(x)$.