write an algebraic expression that could be used to represent the perimeter of the triangle below. write the expression in simplest form.
triangle
3x+1 3-x
2x+4
A: 6x+2
B: 5x-8
C: 4x+8
D: 6x-2
3x+1 + 3-x + 2x+4 = 4x+8.
6x+3
To find the perimeter of a triangle, we need to add up the lengths of all three sides.
The first side of the triangle is 3x + 1.
The second side is 3 - x.
The third side is 2x + 4.
To find the expression for the perimeter, we can simply add up the lengths of these three sides:
Perimeter = (3x + 1) + (3 - x) + (2x + 4)
Now let's simplify the expression:
Perimeter = 3x + 1 + 3 - x + 2x + 4
Combining like terms, we get:
Perimeter = 3x - x + 2x + 1 + 3 + 4
Simplifying further:
Perimeter = 6x + 8
Therefore, the expression in simplest form that represents the perimeter of the triangle is 6x + 8.
The correct answer is C: 6x + 8.
To find the perimeter of the triangle, you need to add up the lengths of all three sides.
The lengths of the sides of the triangle are given as 3x+1, 2x+4, and 3-x.
So, you can write the expression for the perimeter as:
(3x+1) + (2x+4) + (3-x)
Now, simplify the expression by combining like terms:
3x + 1 + 2x + 4 + 3 - x
Combine the x terms:
3x + 2x - x = 4x
Combine the constants:
1 + 4 + 3 = 8
The simplified expression for the perimeter of the triangle is:
4x + 8
So, the correct answer is C: 4x + 8.