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.
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The length and width of the rectangular fence is 6 feet and 1 feet respectively.
Step-by-step explanation:
Let the length of the rectangular fence = L feet
Width of a rectangular fence is 5 feet less than the length.
Let width of a rectangular fence = W = (L - 5) feet
Area of the rectangular fence = L x W = L(L - 5) feet²
If length is decreased by 3 feet.
New length = L = L - 3 feet
New width is increased by 1 feet = W = (L - 5) + 1 = L - 4 feet
New area = L x W = (L - 3)(L - 4) feet²
The area limited by the new fence will be the same as the area of the original fence.
L(L - 5) = (L - 3)(L - 4)
=> L² - 5L = L² - 4L - 3L + 12
=> L² - 5L = L² - 7L + 12
=> 7L - 5L = 12
=> 2L = 12
=> L = = 6 feet
W = L - 5 = 6 - 5 = 1 feet
Hence, the length and width of the rectangular fence is 6 feet and 1 feet respectively.
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