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

26 feet

Step-by-step 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

length of a rectangle deck = l = 26 square

width of a rectangle deck = w = 22 square

Step-by-step 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)

    or    

    or    

As length is always positive so, square

w = 26 - 4

w = 22 square