Question

On the set of ones below triangle KLM has vertices whose coordinates are K(-6,-2) L(6,-4) M(2,6) What is the perimeter of triangle?

Answer 1

Answer:
`2√(37)+2√(29)+8√(2)\ \text{units}`

Explanation:

Given

The coordinates of the triangle are
`K(-6,-2),L(6,-4),M(2,6)`

Distance between the two points is given by the distance formula

`d=√(\left( x_2-x_1\right)^2+\left( y_2-y_1\right)^2)`

Distance between K and L

`KL=√(\left( 6+6\right)^2+\left( -4+2\right)^2)\\KL=√(\left( 12\right)^2+\left( -2\right)^2)\\KL=√(144+4)\\KL=√(148)\ \text{units}`

For L and M

`LM=√(\left( 2-6\right)^2+\left( 6+4\right)^2)\\LM=√(\left( -4\right)^2+\left( 10\right)^2)\\LM=√(16+100)\\LM=√(116)`

For K and M

`KM=√(\left( 8\right)^2+\left( 8\right)^2)\\KM=√(64+64)\\KM=8√(2)\ \text{units}`

The perimeter of the triangle is

`\Rightarrow √(148)+√(116)+8√(2)\\\\\Rightarrow 2√(37)+2√(29)+8√(2)\ \text{units}`