A fence is to have 3 1/2” wide boards
between two posts that are 94 1/4” apart so
that the space between each board is the
same. Calculate the number of boards and
the spacing so that the spacing between the
boards is as small as possible. Round your
answer for the spacing to the nearest 16th of
an inch.

answer:

3 7/8 inches.

Step-by-step explanation:

1 picket = 3 inches

Step 2

Multiply the individual picket width by the number of pickets to find the total area that will be occupied by the pickets.

3 inches x 13 pickets = 39 inches

Step 3

Measure the total width of the installation area. For example, if your fence posts are installed about 6 feet apart and you will install the pickets between the posts, measure the distance between the insides of two adjacent posts.

Total installation width = 68 inches

Step 4

Subtract the total area occupied by pickets from the total installation width. The result tells how much area you have leftover for spaces.

68 inches - 39 inches = 29 inches

Step 5

Divide the total area for the spaces by the number of spaces. This is specific to your layout. For example, since your pickets will be installed between the posts, you'll probably want to have a space next to each post; therefore, you'll need one more space than the number of pickets. If there are 13 pickets, that means 14 spaces:

29 inches divided by 14 spaces = 2.07 inches

The width of each space is 2 inches (rounded).

Alternatively, if you want to install the outer pickets up against the posts, you will need one fewer space than the number of pickets:

29 inches divided by 12 spaces = 2.42 inches

The width of each space is 2 7/16 inches (see Tip below for conversion).

Unit Calculation for Specific Spacing

Step 1

Measure the width of each piece, and then add the desired space dimension to find the unit width. For this example, use 2-inch-wide balusters that must be spaced no more than 4 inches apart.

2 + 4 = 6 inches

6 inches is the unit width.

Step 2

Measure the total width of the installation area. For example, if your railing posts are installed about 4 feet apart and you will install the balusters between the posts, measure the distance between the insides of two adjacent posts.

Total installation width = 45 inches

Step 3

Divide the total installation width by the unit width. The result gives you an estimate of how many balusters you will need.

45 inches divided by 6 (unit dimension) = 7.5 units

Because you can't have less than a whole unit (for even spacing), round up to the next whole number of units.

8 units

Step 4

Recalculate the unit width to find the width of each space. First, multiply the baluster width by the number of balusters to find the total area occupied by the balusters.

8 balusters x 2 inches (baluster width) = 16 inches

Next, subtract the baluster area from the total installation width to find the total area occupied by spaces.

45 inches - 16 inches = 29 inches

Finally, divide the total width of the space area by the number of units.

29 inches divided by 8 = 3.625 inches

The width of each space is 3 5/8 inches (see Tip above for conversion).

Step 5

Recalculate again if you want to have a full space at both ends of the baluster section. The above calculation uses 8 full units consisting of one baluster and one space. However, if you want to have a space between each post and each outer baluster, you can recalculate using 7 balusters and 8 spaces.

7 balusters x 2 inches = 14 inches (total area occupied by balusters)

45 inches - 14 inches = 31 inches (total width occupied by spaces)

31 inches divided by 8 spaces = 3.875 inches

The width of each space is 3 7/8 inches.

the perimeter is increased by a factor of 2

answer: a and b

step-by-step explanation: