# A triangular plot is made by the intersection of x + 2y = 3, 3x - y = 1 and x + y = 0. What is the cost of fencing it at $5/m.

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### 1 Answer

The points at which the given lines intersect to form the triangle can be determined by solving each system of simultaneous equations.

x + 2y = 3 ...(1)

3x - y = 1 ...(2)

Substituting x = 3 - 2y in (2)

3(3 - 2y) - y = 1

=> 9 - 6y - y = 1

=> -7y = -8

=> y = 8/7

x = 5/7

The point is (5/7, 8/7)

3x - y = 1...(1)

x + y = 0 ...(2)

Substitute x = -y in (1)

=> -3y - y = 1

=> y = -1/4

x = 1/4

The point is (1/4, -1/4)

x + 2y = 3 ...(1)

x + y = 0 ...(2)

Substituting x = -y in (1)

=> -y + 2y = 3

=> y = 3

x = -3

The point is (-3, 3)

The perimeter of the triangle is:

`sqrt((-3 - 1/4 )^2 + (3 +1/4 )^2) + sqrt((-3 -5/7 )^2 + (3 - 8/7)^2) + sqrt((5/7 - 1/4)^2 + (8/7 + 1/4)^2)`

= 10.217

It is assumed that this length is in meters. That gives the cost of fencing the plot as 10.217 m * (5$/m) = $51.09

**The required cost of fencing the plot is $51.09.**