Question

What is the perimeter of this triangle?

A
33 units

B
36 units

C
39 units

D
42 units

Answer 1

B

Explanation:

the perimeter of the triangle is the sum of the 3 sides

the horizontal side has endpoints (- 4, 5 ) and (8, 5 )

note that the y- coordinates are both 5 so the length of the line is the absolute value of the difference in the x- coordinates , that is

| 8 - (- 4) | = | 8 + 4 | = | 12 | = 12

the vertical side has endpoints (8, 5 ) and (8, - 4 )

note that the x- coordinates are are both 8, so the length of the line is the absolute value of the difference in the y- coordinates , that is

| - 4 - 5 | = | - 9 | = 9

the inclined side can be calculated using the distance formula

d =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2 }`

with (x₁, y₁ ) = (- 4, 5 ) and (x₂, y₂ ) = (8, - 4) ← endpoints

d =
`√((8-(-4))^2+(-4-5)^2)`

=
`√((8+4)^2+(-9)^2)`

=
`√(12^2+81)`

=
`√(144+81)`

=
`√(225)`

= 15

then

perimeter = 12 + 9 + 15 = 36 units