bertrand is building in the form of a rectangle. he knows that the garden will be 10 feet wide. he wants to fence in the garden but only has 56 feet of fence to work with.

how long mist the garden be to fence it with exactly 56 feet of fence? show how you found your answer.

in order to support the fence, a post must be placed on the 4 corners of the rectangle and every 2 feet along the perimeter. how many posts must bertrand use? show how you found your answer.

if fencing costs $7.00 a foot and posts cost $5.00 each, how mush will it cost to erect the fence? show your work.

P = 2L + 2W

56 = 2L + 2(10)
56 = 2L + 20
36 = 2L
36/2 = L

How do you think the rest of this problem can be solved?

2+2+20=24x10=240

36/2=18

To find the length of the garden that can be fenced with exactly 56 feet of fence, we need to consider that a rectangular garden has two equal sides and two equal widths. We are given that the width is 10 feet.

1. Let's assume the length of the garden is L feet.

2. The perimeter of the garden is given by the formula: Perimeter = 2 * (Length + Width).

Perimeter = 2 * (L + 10).

3. We are also told that Bertrand has only 56 feet of fence, so the perimeter of the garden must be equal to 56 feet:

56 = 2 * (L + 10).

4. Now, let's solve this equation for L:

56 = 2L + 20.

2L = 36.

L = 18.

Therefore, the length of the garden must be 18 feet in order to fence it with exactly 56 feet of fence.

Now, let's find the number of posts Bertrand needs to support the fence.

1. The fence has posts at the 4 corners, so there are 4 corner posts.

2. Along each side, there is a post every 2 feet. Since there are 2 widths and 1 length, we need 2 posts every 2 feet.

3. The total number of posts needed is given by the formula: Posts = 4 + 2 * (Length/2 + Width/2).

Posts = 4 + 2 * (18/2 + 10/2).

Posts = 4 + 2 * (9 + 5).

Posts = 4 + 2 * 14.

Posts = 4 + 28.

Posts = 32.

Bertrand needs 32 posts to support the fence.

Finally, let's calculate the total cost of erecting the fence.

1. The cost of the fence itself is $7.00 per foot, and the length of the garden is 18 feet.

Fence cost = $7.00 * 18.

2. The cost of the posts is $5.00 per post, and Bertrand needs 32 posts.

Posts cost = $5.00 * 32.

3. The total cost is the sum of the fence cost and the posts cost:

Total cost = Fence cost + Posts cost.

Total cost = ($7.00 * 18) + ($5.00 * 32).

Total cost = $126.00 + $160.00.

Total cost = $286.00.

Therefore, it will cost $286.00 to erect the fence.