Amount - Land, Number - Pickets

[Guest]

Another fence related problem:

A square tract of land is to be fenced with 3 inch wide pickets. If the pickets were placed 3 inches apart, 50 pickets would be left over. If the pickets were placed 2.5 inches apart, 50 additional pickets would be needed. Determine amount of land and number of pickets.

I know the tract of land would have equal sides due to being square.

How do I proceed ?

[Guest]

Let P = Number of pickets we have got .........
Then if 6 inch space (P - 50) required for fence
If 5.5 inch space (P + 50) required for fence
Then the length of the perimeter fence of the (assumed square) tract will be the number of pickets times the spacing (picket width + space apart)
Its the same tract of land so both will equal

6(P-50) = 5.5(P+50)
6P - 300 = 5.5P + 275
0.5P = 575
P = 1150

At 6 inch spacing pickets needed is 1100
At 5.5 inch spacing pickets needed is 1200

Length of side is (6 x 1100) / 4 = (6600 / 4) = 1650 inches or 137.5 feet
Area is 18906.25 sq feet = 2100.694 sq yards = 0.434 acres

[Guest]

I don't understand the 6 inch and 5.5 inch spacing.

[Guest]

"fenced with 3 inch wide pickets. If the pickets were placed 3 inches apart,"

I dont know what pickets are????
I assumed they were bits of the fence that were 3 inches wide

Then they are suppused to be 3 inches apart...I assume that means the space between them is 3 inches, So if picket is 3 inches wide and space is 3 inches then from the edge of one picket to the same edge of the next picket will be 6 inches ....the width of the picket + the space to the next.

Similary if 2.5 space then the space taken by a picket and its space apart to next will be 5.5.

You may tell me what pickets are and how they are put in the fence

[Guest]

I understand now. Thanks.

Pickets are the slats used for the fence. Some are in the shape of an upside down " V " at the top and others are flat across the top. Picket fences are common in the U.S. They are very nice fences. Most are mainly wood or vinyl.