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son4ous [18]
3 years ago
13

A dog trainer is trying to find a triangular area behind his house that encloses 1800 square feet for his dog to run. He has the

first two fence posts at (6, 0) and at (0, 25). The final fence post is on the property line at x = 30. Find the point where the trainer can place the final fence post.
Mathematics
1 answer:
aliina [53]3 years ago
7 0

Answer:

C = (30,500)

Step-by-step explanation:

Given

Area = 1800ft^2

A = (6,0)

B = (0,25)

C(x,y) = (30,y)

Required

Determine the coordinates of C

The area of triangle is calculated as thus:

Area = \frac{|A_x(B_y - C_y) + B_x(C_y - A_y) + C_x(A_y - B_y)|}{2}

This gives:

1800= \frac{|6(25 - y) + 0(y - 0) + 30(0 - 25)|}{2}

1800= \frac{|6(25 - y) + 30(0- 25)|}{2}

1800= \frac{|6(25 - y) + 30(-25)|}{2}

1800= \frac{|150 - 6y -750 |}{2}

1800= \frac{|150  -750- 6y |}{2}

1800= \frac{|-600- 6y |}{2}

Multiply through by 2

2 * 1800= |-600- 6y|

3600= |-600- 6y|

3600= |-(600+ 6y)|

3600= 600+ 6y

Solve for 6y

6y = 3600 - 600

6y = 3000

Solve for y

y = 3000/6

y = 500

Hence:

The point is:

C = (30,500)

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