Question

The lengths of the sides of a triangle are, in units, (2-x)/(2x+6),(2x)/(2x+6), and (1)/(2x+6). What is the perimeter of the triangle in simplest terms (in units)?

A. (1)/(2)
B. (3+x)/(2x+6)
C. -(1)/(2)
D. (27+3x)/(2x+6)

Answer 1

`\boxed{\tt B.\:\: (3+x)/(2x+6)}`

Explanation:

Note:

Perimeter of triangle = sum of All sides.

For the question:

`\tt Side \:\:1= (2-x)/(2x+6)`

`\tt Side\:\:2=(2x)/(2x+6)`

`\tt Side\:\:3=(1)/(2x+6)`

Now

Perimeter of triangle= sum of all sides

= Side 1+ side 2+ side 3

=
`\tt (2-x)/(2x+6)+ (2x)/(2x+6)+ (1)/(2x+6)`

=
`\tt (2-x+2x+1)/(2x+6)`

=
`\tt (3+x)/(2x+6)`

Therefore, The perimeter of the triangle in simplest terms :
`\boxed{\tt B.\:\: (3+x)/(2x+6)}`