Question

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

Answer 1

Answer:

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)

$572 = l^{2} - 4l$

$l^{2} - 4l - 572 = 0$

$l^{2} - 26l + 22l - 572 = 0$

$(l^{2} - 26l) + (22l - 572) = 0$

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

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

$l - 26=0$     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

Answer:

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