Question

The robertsons put a rectangular pool with a stone walkway around it in their backyard. The total length of the pool and walkway is 3 times the total width. The walkway is 2 ft wide all around

Answer 1

Answer:

115 square feet.

Step-by-step explanation:

Please consider the complete question.

The Robertsons put a rectangular pool with a stone walkway around it in their backyard. The total length of the pool and walkway is 3 times the total width. The walkway is 2 ft wide all around. Find the area of the pool when the total width is 9 ft.

Let w represent width of pool.

Since total length of the pool and walkway is 3 times the total width, so total length of pool and walkaway would be $3w$.

Since walkway is 2 ft wide all around, so length and width of pool will be 4 feet less that is width would be $w-4$ and length would be $3w-4$.

We know that area of rectangle is length times width, so we will get:

$\text{Area of pool}=(3x-4)(x-4)$

$\text{Area of pool}=3w^2-12w-4w+16$

$\text{Area of pool}=3w^2-16w+16$

To find the area of pool, when total width is 9 ft, we will substitute $w=9$ in our area equation as:

$\text{Area of pool}=3(9)^2-16(9)+16$

$\text{Area of pool}=3(81)-144+16$

$\text{Area of pool}=243-144+16$

$\text{Area of pool}=115$

Therefore, the area of pool would be 115 square feet.