Question

You want to put a fence around your large yard. There are two companies that you have found to 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.
TREE Position (relative to your house)
1 100 ft. east 2 40 ft east, 80 ft south 3 40 ft west, 120 ft south 4 90 ft west, 60 ft north 5 20 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 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 of the sides.
STEP 4: Company 1 says that they will complete the job for $12 per foot of fencing. Company 2
says that they will charge you $250 for the first 100 feet of fencing and $15 for each additional foot. Determine the cost of fencing for both companies.

Answer 1

Answer:

STEP 1: See attached drawing  on graph paper

STEP 2:

Length of segment 1 - 2 = 100 feet

Length of segment 2 - 3 = 89.44 ft.

Length of segment 3 - 4 = 186.82 ft.

Length of segment 4 - 5 = 120.83 ft.

Length of segment 5 - 1 = 136.01 ft.

STEP 3:

The perimeter of the property is 633.103 ft.

STEP 4:

The cost of fencing by Company 1 is $7597.24

The cost of fencing by Company 2 is $8246.55

Therefore, the company that provides the cheapest quote for fencing the property is Company 1

Step-by-step explanation:

STEP 1: See attached drawing  on graph paper

STEP 2:

Therefore, we have

Length of segment 1 - 2 = √(8² + 6²) = 10 × 10 = 100 feet

Length of segment 2 - 3 = √(4² + 8²) = 4·√5× 10 = 40·√5 feet = 89.44 ft.

Length of segment 3 - 4 = √(5² + 18²) = √349 = 10·√349 feet = 186.82 ft.

Length of segment 4 - 5 = √(11² + 5²) = √146 = 10·√146 feet = 120.83 ft.

Length of segment 5 - 1 = √(11² + 8²) = √185 = 10·√185 feet = 136.01 ft.

STEP 3:

Therefore, the perimeter of the property = 100 + 89.44  + 186.82 + 120.83  + 136.01  = 633.103 ft.

STEP 4:

Hence the cost of fencing the property by Company 1 = $12 × 633.103 = $7597.24

The cost of fencing the property by Company 2 = $250 + $15 × 533.103 = $8246.55.