Answer:
Width = 60
Length = 85
Step-by-step explanation:
Let L represent the length of the rectangular plot.
From the information given, the plot has a width that is 25 meters less than its length. This means that
Width = L - 25
Recall, the formula for calculating the area of a rectangle is expressed as
Area = length x width
If the area of the plot is 5100 square meters, the required equation would be
L(L - 25) = 5100
By expanding the parentheses, it becomes
L^2 - 25L = 5100
L^2 - 25L - 5100 = 0
This is a quadratic equation. We would solve by applying the method of factorization. The first step is to multiply L^2 with - 5100. It becomes - 5100L^2. We would find two terms such that their sum or difference is - 25L and their product is - 500L^2. The terms are 60L and - 85L. By replacing - 25L with 60L - 85L, we have
L^2 + 60L - 85L - 5100 = 0
We would factorize by grouping. It becomes
L(L + 60) - 85(L + 60) = 0
Since L + 60 is common, it becomes
(L + 60)(L - 85) = 0
L + 60 = 0 or L - 85 = 0
L = - 60 or L = 85
The length cannot be negative. Thus,
L = 85
Substituting L = 85 into Width = L - 25,
Width = 85 - 25
Width = 60
Length = 85