Question

Amy and Zach each have 24 feet of fencing for their rectangular gardens. Amy makes her fence 6 feet long . Zach makes his fence 8 feet long . Who’s garden has a greater area ? How much greater ?

Answer 1

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

$P=2(L+W)$

step 1

Rectangular garden of Amy

we have

$P=24\ ft\\L=6\ ft$

substitute in the formula of perimeter

$24=2(6+W)$

solve for W

simplify

$12=(6+W)\\W=6\ ft$

Find the area

Remember that the area is equal to

$A=LW=(6)(6)=36\ ft^2$

step 2

Rectangular garden of Zach

we have

$P=24\ ft\\L=8\ ft$

substitute in the formula of perimeter

$24=2(8+W)$

solve for W

simplify

$12=(8+W)\\W=4\ ft$

Find the area

Remember that the area is equal to

$A=LW=(8)(4)=32\ ft^2$

step 3

Find the difference of the areas

$36-32=4\ ft^2$

therefore

Amy's garden has the greater area by 4 square feet

Answer 2

For this case we have that by definition, the area of a rectangle is given by:

$A = w * l$

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 $P = 2w + 2l = 24.$

Amy:

$l = 6 \ ft\\2w + 2 (l) = 24\\2w + 2 (6) = 24\\2w + 12 = 24\\2w = 24-12\\2w = 12\\w = 6$

Thus, Amy's fence area is: $A = 6 * 6 = 36 \ ft ^ 2$

Zach:

$l = 8 \ ft\\2w + 2l = 24\\2w + 2 (8) = 24\\2w + 16 = 24\\2w = 24-16\\2w = 8\\w = 4$

Thus, the area of Zach's fence is:$A = 4 * 8 = 32 \ ft ^ 2$

Answer:

Amy's garden has a greater area

$36 \ ft ^ 2-32 \ ft ^ 2 = 4ft ^ 2$, is $4 \ ft ^ 2$greater