Answer:Smaller value is 4 yards.
The larger value is 6 yards.
Step-by-step explanation:
Let L represent the length or larger value of the rectangular plot.
Let W represent the width or smaller value of the rectangular plot.
The area of the rectangular field is expressed as
LW = 24 - - - - - - - - - - 1
The formula for determining the perimeter of the rectangular fence is expressed as
2(L + W) = 20
L + W = 20/2 = 10
Substituting L = 10 - W into equation 1, it becomes
W(10 - W) = 24
10W - W² = 24
W² - 10W + 24 = 0
W² - 6W - 4W + 24 = 0
W(W - 6) - 4(W - 6) = 0
W - 4 = 0 or W - 6 = 0
W = 4 or W = 6
Substituting W = 4 and W = 6 into
L = 10 - W, it becomes
L = 10 - 4 or L = 10 - 6
L = 6 or L = 4
