For this case we have that by definition, the area of a rectangle is given by:
[tex]A = w * l[/tex]
Where:
w: Is the width of the rectangle
l: is the length of the rectangle
Each of the girls has 24 feet of fencing, that is, the perimeter is [tex]P = 2w + 2l = 24.[/tex]
Amy:
[tex]l = 6 \ ft\\2w + 2 (l) = 24\\2w + 2 (6) = 24\\2w + 12 = 24\\2w = 24-12\\2w = 12\\w = 6[/tex]
Thus, Amy's fence area is: [tex]A = 6 * 6 = 36 \ ft ^ 2[/tex]
Zach:
[tex]l = 8 \ ft\\2w + 2l = 24\\2w + 2 (8) = 24\\2w + 16 = 24\\2w = 24-16\\2w = 8\\w = 4[/tex]
Thus, the area of Zach's fence is:[tex]A = 4 * 8 = 32 \ ft ^ 2[/tex]
Answer:
Amy's garden has a greater area
[tex]36 \ ft ^ 2-32 \ ft ^ 2 = 4ft ^ 2[/tex], is [tex]4 \ ft ^ 2[/tex]greater
Answer:
Amy's garden has the greater area by 4 square feet
Step-by-step explanation:
we know that
The perimeter of a rectangle is given by the formula
[tex]P=2(L+W)[/tex]
step 1
Rectangular garden of Amy
we have
[tex]P=24\ ft\\L=6\ ft[/tex]
substitute in the formula of perimeter
[tex]24=2(6+W)[/tex]
solve for W
simplify
[tex]12=(6+W)\\W=6\ ft[/tex]
Find the area
Remember that the area is equal to
[tex]A=LW=(6)(6)=36\ ft^2[/tex]
step 2
Rectangular garden of Zach
we have
[tex]P=24\ ft\\L=8\ ft[/tex]
substitute in the formula of perimeter
[tex]24=2(8+W)[/tex]
solve for W
simplify
[tex]12=(8+W)\\W=4\ ft[/tex]
Find the area
Remember that the area is equal to
[tex]A=LW=(8)(4)=32\ ft^2[/tex]
step 3
Find the difference of the areas
[tex]36-32=4\ ft^2[/tex]
therefore
Amy's garden has the greater area by 4 square feet
