Question

Triangle ABC is shown on the grid.

What is the perimeter of triangle ABC?

9 + units
9 + units
9 + units
9 + units

Answer 1

its 9 + the square root of 41

Answer 2

Answer: The third option is correct and the perimeter of ABC is
`9+√(41)`.

Step-by-step explanation:

The vertices of the triangle are A(-1,5), B(4,5) and C(-1,1).

Use distance formula to find the length of all sides of the triangle.

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

`AB=√((4-(-1))^2+(5-5)^2)= √((4+1)^2+0) =5`

`BC=√((-1-4)^2+(1-5)^2)= √(25+16)= √(41)`

`AC=√((-1-(-1))^2+(1-5)^2)= √(0+16)=4`

Therefore the length of sides are
`5,√(41),4` units.

Perimeter is the sum of length of all sides.

Perimeter of ABC is,

`S=AB+BC+AC`

`S=5+√(41)+4`

`S=9+√(41)`

Therefore, the third option is correct and the perimeter of ABC is
`9+√(41)` units.