You want to put a fence around your large yard. You have found two companies that can do the work. They have each given you a quote for how much the work will cost. Of course, you want to find out which company will be the cheapest. The boundary of your yard is determined by five trees. The lines connecting them form the edge of your property. Shown below are the descriptions for the positions of the trees relative to your house.

TreePosition (Relative to your house)
1100 ft. East
240 ft. East, 80 ft. South
340 ft. West, 120 ft. South
490 ft. West, 60 ft. North
520 ft. East, 110 ft. North

Step 1: On graph paper, mark the position of each of the trees on your land. Let each block of the graph paper represent a 10-foot by 10-foot square. Using a straightedge, connect Tree 1 to Tree 2, Tree 2 to Tree 3, Tree 3 to Tree 4, and so on.

Step 2: Use the Pythagorean Theorem (or distance formula) to find the length of each side of your property. Round each answer to the nearest hundredth, if necessary.

Step 3: Determine the perimeter of your property by adding up all the sides.

Step 4: Company 1 says they will complete the job for $12 per foot of fencing. Company 2 says they will charge $4,600 for the first 550 feet of fence and $29 for each additional foot. Determine the cost of fencing for both companies.

Step 5: Figure out which company will complete the job for the least amount of money.

Break your property into smaller parts and use the Pythagorean Theorem to find the length for each side. Remember that each grid line on your graph paper represents 10 feet. Also remember to round to the nearest hundredth, if necessary. Show your work below.

Work for the distance from Tree 1 to Tree 2

Distance: _ ft. Work for the distance from Tree 2 to Tree 3

Distance: _ ft.
Work for the distance from Tree 3 to Tree 4

Distance: _ ft. Work for the distance from Tree 4 to Tree 5

Distance: _ ft.
Work for the distance from Tree 5 to Tree 1

Distance: _ ft. Work for the perimeter of your property.

Distance: _ ft.

•Company 1 charges $12 per foot of fence. Find the cost if Company 1 completes the job. Show work!

Cost: $_

•Company 2 charges $4,600 for the first 550 feet of fence and $29 for each additional foot. Find the cost if Company 2 completes the job. Show work!

Cost: $_

•Both companies must charge a 6% sales tax. Determine which company will be the cheapest. Then, find the cost including the tax. Round to the nearest cent. Show work!

Cost: $_