Length- Boards

[Guest]

5 boards high does not come to 7.5 feet fence height. if horizontal

8 feet long boards vertically does not mean 7.5 feet fence height

You need to describe this sensibly and ask a sensible question

[Guest]

I don't know.

[Guest]

If what you say here is correct.......
............................
Boards are placed horizontally, 5 boards high.

Boards are placed vertically, 1 inch spacing.

Use 2 x 4 boards, 8 feet in length.
...............................................................

I assume you mean board thickness is 2 inches and board width is 4 inches
Then horizontal boards, 5 boards high is 5 x 4 = 20 inches high or 1 foot 8 inches high fence
...............OR
If vertical boards 8 foot long then the height of the fence would be 8 feet except if you cut 6 inches off each board
and at 1 inch spacing then each board plus 1space would take up 5 inches.

[Guest]

Try:

Boards are placed horizontally, 4 boards high.

Boards are placed vertically, 1/4 inch spacing.

Use 1 by 2 boards, 3 feet in length.

[Guest]

This does not make up a fence??????????????????????????????

Boards are placed horizontally, 4 boards high.

Boards are placed vertically, 1/4 inch spacing.

Use 1 by 2 boards, 3 feet in length.

[Guest]

I don't know.

[Guest]

If the boards are fixed vertically then the length of the board will be the vertical height and the spacing will be the spaces between each board.

If the boards are fixed horizontally then the boards will be fixed end to end lengthwise around the garden. There will be no spacing end to end. The vertical spacing between horizontal boards will depend on the height of the fence or top board and how many boards are in between.

[Guest]

I understand.

So, the fence has to be at least 40.5 feet in length, 30.25 feet in width, and 7.5 feet in height.


Any suggestions ?

[Guest]

The fence is installed around the perimeter of the garden. It does not cover the area of the garden, it goes around it. Its length will be the total length of the 4 sides of the garden added together. It is not multiplied as in finding the area of the garden. The height of the fence will simply be the height of the fence as in say the height of a fence post or the heigth of a panel between posts et....you say you want it 7.5 feet high.

"So, the fence has to be at least 40.5 feet in length, 30.25 feet in width, and 7.5 feet in height." ????????
Why do you say "at least " 40.5 feet in length, 30.25 feet in width..?????

[Guest]

Typo error.

[Guest]

So, the fence will be 40.5 + 40. 5 + 30.25 + 30. 25 = 141.5 feet + 7.5 feet high.

[Guest]

"So, the fence will be 40.5 + 40. 5 + 30.25 + 30. 25 = 141.5 feet "......That will be the distance around the outside of the garden......Where is the fence.???????


"+ 7.5 feet high. "......This is the height you say the fence is to be...????....does that add to the distance around the garden to make it longer...??????

[Guest]

"......Where is the fence.???????" Outside of the garden.


"+ 7.5 feet high. "......This is the height you say the fence is to be...????....does that add to the distance around the garden to make it longer...??????" No - height of fence given in problem.

[Guest]

"......Where is the fence.???????" Outside of the garden.......No it is around the perimeter or outer edge of the garden....

"+ 7.5 feet high. "......This is the height you say the fence is to be...????....does that add to the distance around the garden to make it longer...??????" No - height of fence given in problem.......Then why did you add it to the perimeter....?????

You still have not asked a sensible question yet....... You have not said how the fence is constructed to make it 7.5 feet high.
Are the boards horizontal OR vertical OR at an angle. Do they fit end to end or sideways. Are they tight together of spaced out..... OR whatever other information needed to describe the construction of the fence.

[Guest]

I don't know to calculate the answer.

[Guest]

"I don't know to calculate the answer".......The problem is you don't know to ask the question.......

...This is the original question
"A garden 40.5 feet in length and 30.25 feet in width, is to be enclosed with a fence. The fence is 7.5 feet in height. Determine number of boards needed."

We cannot workout the number of boards until you tell us the dimensions of the boards and how the boards are put on the fence.
And...in describing this it needs to be able to make the fence 7.5 feet high.

If the boards are 8 ft long and fitted vertical then 6 inches needs to be cut off each board as the board will be too high. The vertical boards can be fitted side by side tight or with spacing and this width and spacing matters as to how many boards will be needed.

If the boards are 8 feet long and fitted horizontal and put end to end around the fence then 8 feet long boards are not a problem but the width of the boards matters and the vertical spacing matters as to how many make up 7.5 feet.

This is the information you need to provide with the question.

[Guest]

Try:

Length of boards - 7.5 feet.

Spacing - 1/4 inch for one situation and side by side for another situation.

Boards to be placed vertical.


For horizontal placing:

Length of boards - 7. 5 feet.

Width of boards - 3 inches.

5 boards high.

[Guest]

Yes, The question is now more complete and making more sense. You did not give the width of the board for the first example (I will take it as 3 inches as in second example). We should have enough information now to solve. I would have thought by now that you would at least have been able to attempt to answer the question yourself. I will explain how to solve each example.....


Garden perimeter is 2(40.5 + 30.25) = 141.5 feet around the whole garden

First fence example.....

Vertical boards 7.5 feet long/high, 3 inch wide, tight side by side, number of boards is 141.5 x 12 / 3 = 566 boards.

For same board but 1/4 inch spacing between each board, number of boards is 141.5 x 12 / 3.25 = 522 boards (rounding to nearest)

Second fence example..........

Horizontal boards 7.5 feet long, Assume no board on bottom at ground level and top board at 7.5 feet high. 5 boards high we will call each a rail so 5 rails high. The number of boards in each rail is 141.5 / 7.5 = 19 to nearest. And for 5 rails total boards is 5 x 19 = 95 boards.

For horizontal second example, each (board + space) vertical is (7.5 / 5) = 1.5 feet = 18 inches, so vertical space between boards is 15 inches. because board is 3 inches width.

[Guest]

Thanks.

"I would have thought by now that you would at least have been able to attempt to answer the question yourself." I was not sure how to solve.

[Guest]

I thought you might be interested in what wastage you may have when fencing each side of the garden separately, the way it would be done if actually doing it in practice.
When you come to the end of one side you may have to cut a board and the piece cut off may be no good to be used anywhere else so you would have wastage and need more boards.

Working out how many for each side separately gives this answer.............

40.5 / 7.5 = 5.4 boards, This is 5 full boards and a piece 0.4 x 7.5 = 3 feet at the end.....assuming this short piece can be fixed OK.
So we actually need 6 boards and cut off 0.6 x 7.5 = 4.5 feet. This 4.5 feet piece is longer than the 3 foot piece that will be needed for the other side so 3 feet will need to be cut off this piece for the end of the other side and leave 1.5 feet as wastage. There will be 5 pieces (1 for each rail) of 1.5 feet wastage = 7.5 feet.....actually the length of 1 board if it had not been cut up. So that means we need 11 boards for each rail on the 2 long sides of the garden and there are 5 rails, so 55 boards needed.

For the short sides of the garden..............
30.25 / 7.5 = 4.0333 x 2 x 5 rails = 40 boards with 10 x 0.0333 pieces cut off = 0.3 x 7.5 = 2.25 feet wastage

total boards = 55 + 40 = 95 boards. The same as before, so not enough wastage to need more boards (because we were able to use some of it) than we had calculated last time when we just simply rounded up the number of boards needed to even numbers.