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Answer: Length is 6 ft and
Width is 1 ft
Step-by-step explanation: The first clue we have been given is that the width of the rectangular fence is five feet less than it's length. So, if the length is L, the width is L - 5. From that bit of information on we can calculate the area if he rectangular fence as
Area = L x W
Area = L x (L - 5)
Area = L² - 5L
Also, the question further states that if the length is decreased by three feet (L = L - 3), and the width is increased by one foot (W = {L - 5} + 1 and that becomes L - 4), the area of the new enclosure would be the same as the first one. The area of the new enclosure would be given as
Area = L x W
Area = (L - 3) (L - 4)
Area = L² - 4L - 3L + 12
Area = L² - 7L + 12
Since the question states that the area of the original fence and the new one are the same, we can now write the following expression
L² - 5L = L² - 7L + 12
(That is, area of the first set of dimensions equals area of the second set of dimensions)
L² - 5L = L² - 7L + 12
By collecting like terms we now have
L² - L² - 5L + 7L = 12
(Note that when a positive value crosses the equation to the other side, it becomes negative and vice versa)
2L = 12
Divide both sides of the equation by 2
L = 6
Having calculated the length of the rectangular fence as 6 ft, the width is now derived as
W = L - 5
W = 6 - 5
W= 1
Therefore, the length is 6 ft and the width is 1 ft.
The length of the original rectangular fence is 6 feet and the width is 1 feet.
Given that,
The width of a rectangular fence is 5 feet less than the length.
If the length is decreased by 3 feet and the width is increased by 1 feet.
The area limited by the new fence will be the same as the area of the original fence.
We have to determine,
The dimensions of the original rectangular fence.
According to the question,
Let the length of the rectangular fence be L,
And the width of the rectangular fence be L-5,
Then the area of the rectangular fence is given by,
[tex]\rm Area = Length \times width[/tex]
Substitute the value in the formula,
[tex]\rm Area = length \times width \\\\Area = L \times (L-5)\\\\Area = L^2-5L[/tex]
If the length is decreased by 3 feet and the width is increased by 1 foot,
Then the new length of the rectangular fence is (L-3)
And the new width of the rectangular fence is (L-5) + 1 = L-4
Again substitute all the values in the formula
[tex]\rm Area = Length \times width\\\\Area = (L-3) \times (L-4)\\\\Area = L(L-4) -3(L-4)\\\\Area = L^2-4L-3L+12\\\\Area = L^2-7L+12[/tex]
Therefore,
The area limited by the new fence will be the same as the area of the original fence,
[tex]\rm Area \ of \ original \ fence = Area \ of \ new \ fence\\\\L^2-5L = L^2-7L+12\\\\L^2-5L-L^2+7L-12=0\\\\2L-12=0\\\\2L=12\\\\L =\dfrac{12}{2}\\\\L=6[/tex]
Therefore, the length of the rectangular fence is 6,
And the width of the rectangular fence be L-5 = 6-5 = 1,
Hence, The length of the original rectangular fence is 6 feet and width is 1 foot.
To know more about Rectangle click the link given below.
https://brainly.com/question/10046743
