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)
[tex]572 = l^{2} - 4l[/tex]
[tex]l^{2} - 4l - 572 = 0[/tex]
[tex]l^{2} - 26l + 22l - 572 = 0[/tex]
[tex](l^{2} - 26l) + (22l - 572) = 0[/tex]
[tex]l(l - 26) + 22(l - 26) = 0[/tex]
[tex](l - 26) (l + 22) = 0[/tex]
[tex]l - 26=0 \\[/tex] or [tex]l+22=0[/tex]
[tex]l =26 \\[/tex] or [tex]l=-22[/tex]
As length is always positive so, [tex]l =26 \\[/tex] square
w = 26 - 4
w = 22 square
