Question

Manuel is building a circular pool with an area of 100 square feet he will build rectangular deck around the pool as shown

The width of the deck will be 4 feet less thAn the length of the deck

Manuel decides to make the total area of the pool and deck 572 square feet what is the length in feet of the deck

Answer 1

length of a rectangle deck = l = 26 square

width of a rectangle deck = w = 22 square

Explanation:

Let,

length of a rectangle deck = l

width of a rectangle deck = w

Given Data:

Area of the deck = 572 square feet

According to given condition;

w = l - 4

To Find Out:

length of a rectangle deck = i = ?

width of a rectangle deck = w = ?

Formula:

Area of a rectangle = A = l × w

Solution:

Area of a rectangle = A = l × w

572 = l × w

572 = l × ( l - 4)

`572 = l^(2) - 4l`

`l^(2) - 4l - 572 = 0`

`l^(2) - 26l + 22l - 572 = 0`

`(l^(2) - 26l) + (22l - 572) = 0`

`l(l - 26) + 22(l - 26) = 0`

`(l - 26) (l + 22) = 0`

`l - 26=0 \\` or
`l+22=0`

`l =26 \\` or
`l=-22`

As length is always positive so,
`l =26 \\` square

w = 26 - 4

w = 22 square

Answer 2

26 feet

Explanation:

w: width

w+4 : length

w(w+4) = 572

w² + 4w - 572 = 0

w² + 26w - 22w - 572 = 0

w(w+26) - 22(w+26) = 0

(w-22)(w+26) = 0

w = 22, -26

width = 22 feet

length = w+4 = 22+4 = 26 feet