Chapter A.8, Problem 36AYU

To determine

To find:

a. If the pond is square, what are its dimensions?

Answer to Problem 36AYU

a. The dimensions are 19 ft.

Explanation of Solution

Given:

A pond is enclosed by a wooden deck that is 3 feet wide. The fence surrounding the deck is 100 feet long.

Calculation:

a. The pond is square so its dimensions are

$4\left(x+6\right)=100$

$4x=76$

$x=19$

Therefore the dimensions are 19.

To determine

To find:

b. If the pond is rectangular and the length of the pond is to be three times its width, what are its dimensions?

Answer to Problem 36AYU

b. Length and width are $9.5\text{ft}$, $28.5\text{ft}$.

Explanation of Solution

Given:

A pond is enclosed by a wooden deck that is 3 feet wide. The fence surrounding the deck is 100 feet long.

Calculation:

b. The pond is rectangular.

So, $2\left(3x+6\right)+2\left(x+6\right)=100$.

$8x=76$

$x=9.5 \text{ft}$ and $28.5 \text{f}$(three times its width)

Therefore length and width are $9.5 \text{ft}$, $28.5 \text{ft}$.

To determine

To find:

c. If the pond is circular, what is its dimensions?

Answer to Problem 36AYU

c. The dimensions would be $25.85 \text{ft}$.

Explanation of Solution

Given:

A pond is enclosed by a wooden deck that is 3 feet wide. The fence surrounding the deck is 100 feet long.

Calculation:

c. The pond is circular.

$C=\pi .d$

That is $C=\pi .\left(d+6\right)$.

$100=\pi .\left(d+6\right)$

$d+6=31.8$

$d=25.85$

To determine

To find:

d. Which pond has the larger area?

Answer to Problem 36AYU

d. The area 525 sq.ft.

Explanation of Solution

Given:

A pond is enclosed by a wooden deck that is 3 feet wide. The fence surrounding the deck is 100 feet long.

Calculation:

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