Triangle abc has a perimeter of 12 units. the vertices of the triangle are a(x,2), b(2,-2), and c(-1,2). find the value of x.

The value of x is 2

Step-by-step explanation:

* Lets explain how to find a distance between 2 points

- If the endpoints of a segment are and

  is

- Triangle ABC has a perimeter of 12 units

∵ The perimeter of any triangle is the sum of lengths of its sides

∴ P Δ ABC = AB + BC + AC

* Lets find the length of the three sides

∵ A = (x , 2) , B = (2 , -2) , C = (-1 , 2)

∵

∴

∴

∵

∴

∴

∴

∴ BC = 5

∵

∴

∴

- The √ is canceled by power 2

∴ CA = (x + 1)

∵ AB + BC + CA = 12

∴ + 5 + (x + 1) = 12

- Add 5 and 1

∴ + 6 + x = 12

- subtract 6 and x from both sides

∴ = (6 - x)

- To cancel (√ ) square the two sides

∴ (2 - x)² + 16 = (6 - x)²

- Simplify the two sides

∴ [(2)(2) + (2)(2)(-x) + (-x)(-x)] + 16 = (6)(6) + (2)(6)(-x) + (-x)(-x)

∴ 4 - 4x + x² + 16 = 36 - 12x + x²

- Subtract x² from both sides

∴ 20 - 4x = 36 - 12x

- Add 12x to both sides and subtract 20 from both sides

∴ 12x - 4x = 36 - 20

∴ 8x = 16

- Divide both sides by 8

∴ x = 2

* The value of x is 2