Chapter A.8, Problem 35AYU

To determine

To find:

a. If the length of the garden is to be twice its width, what will be the dimensions of the garden?

Answer to Problem 35AYU

a. The dimensions are 10 ft by 5 ft.

Explanation of Solution

Given:

A gardener has 46 feet of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it.

Calculation:

a. Length of the garden is to be twice its width.

So, $2\left(w+4\right)+2\left(2w+4\right)=46$.

$6w=30$

$w=5$

Therefore width is 5 and length is 10.

To determine

To find:

b. What will be the area of the garden?

Answer to Problem 35AYU

b. The area is 50 sq.ft.

Explanation of Solution

Given:

A gardener has 46 feet of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it.

Calculation:

b. The area = (width)(length) $=5\left(10\right)=50\text{ sq}\text{.ft}$.

To determine

To find:

c. If the length and width of then garden are to be the same, what will be the dimensions of the garden?

Answer to Problem 35AYU

c. The dimensions would be $7.5\text{ft}$ by $7.5\text{ft}$.

Explanation of Solution

Given:

A gardener has 46 feet of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it.

Calculation:

c. The dimensions of the garden length and width are same.

$2\left(w+4\right)+2\left(w+4\right)=46$

$4w=30$

$w=7.5\text{ft}$

Therefore, the dimensions would be $7.5\text{ft}$ by $7.5\text{ft}$.

To determine

To find:

d. What will be the area of the square garden?

Answer to Problem 35AYU

d. The area would be $56.25\text{sq}\text{.ft}$.

Explanation of Solution

Given:

A gardener has 46 feet of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it.

Calculation:

d. The area of square is $={\left(7.5\right)}^2=56.25\text{sq}\text{.ft}$.