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

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.