SOLUTION: A square lot of land was purchased and a number of 3 inch pickets used to create a fence around it. If the pickets were placed 3 inches apart, 50 pickets are left over. If picket
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Question 1108430: A square lot of land was purchased and a number of 3 inch pickets used to create a fence around it. If the pickets were placed 3 inches apart, 50 pickets are left over. If pickets are placed 2.5 inches apart, 50 more are needed. Determine amt. of land and pickets purchased.
Area of square = s^2
Perimeter = 4s
Not sure how to solve. Non-homework. Answer by ikleyn(52925) (Show Source):
Perimeter = (3+3)*(N-50) (1) ("If the pickets were placed 3 inches apart, 50 pickets are left ove")
Perimeter = (3+2.5)*(N+50) (2) ("If pickets are placed 2.5 inches apart, 50 more are needed")
(Notice that in (1) 3+3 is the distance between "axial lines" of the pickets:
3 in is their width and 3 in is the distance between them)
(same meaning has 3+2.5 in the equation (2) )
==============> 6*N - 300 = 5.5*N + 275,
6N - 5.5N = 300 + 275,
0.5N = 575 ====> N = 1150.
So, N = 1150 pickets were purchased.
Then the perimeter = 6*(N-50) = 6*1100 = 6600 inches.
Hence, the side of the square = = 1650 inches,
Then the area = 1650^2 = 2722500 sq. inches = sq. ft = 18906.25 sq. ft.
