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 ?

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

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

Amy:

Thus, Amy's fence area is:

Zach:

Thus, the area of Zach's fence is:

Amy's garden has a greater area

, is greater

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

step 1

Rectangular garden of Amy

we have

substitute in the formula of perimeter

solve for W

simplify

Find the area

Remember that the area is equal to

step 2

Rectangular garden of Zach

we have

substitute in the formula of perimeter

solve for W

simplify

Find the area

Remember that the area is equal to

step 3

Find the difference of the areas

therefore

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

me

step-by-step explanation: