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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: 80 ft. east 2: 50 ft east, 100 ft south 3: 60 ft west, 120 ft south 4: 70 ft west, 80 ft north 5: 10 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 $14 per foot of fencing. Company 2 says that they will charge you $4600 for the first 500 feet of fencing 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.

Respuesta :

Answer:

STEP 1:

The coordinates of the trees are

A (80, 0), B(50, -100), C(-60, -120), D(-70, 80), E(10, 110)

Drawing a pentagon online

The lengths are

STEP 2:

Length A to B = 10√109

Length B to C =  50√5

Length C to D = 10√401

Length D to E = 10√73

Length E to A = 10√170

STEP 3:

The perimeter = 632.28 ft

STEP 4:

Company 1 Completion of job cost = $8851.93

Company 2 Completion of job cost = $8436.13

STEP 5:

The company that will complete the job with the least amount of money is Company 2

Step-by-step explanation:

STEP 1:

The coordinates of the trees are

A (80, 0), B(50, -100), C(-60, -120), D(-70, 80), E(10, 110)

Drawing a pentagon online

The lengths are

STEP 2:

Length A to B = √((-100 -0)² + (80 - 50)²) = 10√109

Length B to C = √((-60 -50)² + (-100 + 120)²) = 50√5

Length C to D = √((-60 +70)² + (-120 - 80)²) = 10√401

Length D to E = √((-70 -10)² + (80 - 110)²) = 10√73

Length E to A = √((10 -80)² + (110 - 0)²) = 10√170

STEP 3:

The perimeter = 10√109 + 50√5 + 10√401 + 10√73 + 10√170 = 632.28 ft

STEP 4:

Company 1

At $14 per foot, total cost of fencing = 632.28 ft × $14/ft = $8851.93

Company 2

At $4600 for the first 500 feet and $29 for each additional foot, we have;

$4600 + (632.28 - 500) ft ×$29/ft = $8436.13

STEP 5:

Based on cost comparison Company 2 with a cost of $8436.13 is cheaper than company 1 with a cost of $8851.93

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