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. Find the dimensions of the original rectangular fence.

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.

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