You want to put a fence around your large yard.

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: 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.

Answer 1

Hello,

You could solve this through the pythogorous theorem...by letting the hous be at point (0,0) in the graph where the 2 x & y axis intersect. Then,

Tree(a) is at point (80,0)

Tree(b) is at point (50,-100)

Tree(c) is at point (-60,-120)

Tree(d) is at point (-70, 80)

Tree(f) is point (10,110)

Then the distance between A & B ican be calculated from the Graph as

AB = SqRT( [x coordinate distance of Tree(a) from (0,0) - x-coordinate distance of Tree(b) from 0,0)]^2 + [0-100]^2 )

= SqRT( 30^2 + (100)^2)

Similarly, from the graph ===>

BC = SqRT( (110)^2 + (20)^2)

DC = SqRT((10)^2 + (200)^2)

DF = SqRT( (30)^2 + (80)^2)

Once these distances are calculated, you can calculate the answers to the rest of the questions.

Answer 2

You are generating 5 coordinate pairs:

Tree 1 (80,0), Tree 2 (50,-100),Tree 3 (-60,-120), Tree 4 (-70,80) and Tree 5 (10,110)

You can divide each set of coordinates by 10 to plot on graph paper where each square represents 10 by 10, e.g, plot 50, -100 as 5,-10

Use distance formula to find following distances:

Tree 1 to Tree 2

Tree 2 to Tree 3

Tree 3 to Tree 4

Tree 4 to Tree 5

Tree 5 to Tree 1

example of use distance formula for Tree 1 to Tree 2: sqrt[(80-50)^2 + (0 -(-100))^2] = 104

Compute perimeter as sum of distances, say it is x.

Compute cost of company 1: 14 * x

Compute cost of company 2: 4600 + (x-500)*29

Pick whatever company has the lowest price