n a triange the longest side is 2 more than the shortest side. the third side is half of the sum of the longest side, then express the perimeter in polynomial form

well, two sides are x and x+2

I have no idea what half of the sum of the longest side might mean. A sum involves the addition of two numbers.

Let's assume the shortest side of the triangle is represented by the variable "x".

According to the given information, the longest side will be "2 + x" and the third side will be "(2 + x)/2".

The perimeter of a triangle is the sum of all its sides. Therefore, the perimeter can be expressed as:

Perimeter = shortest side + longest side + third side

Perimeter = x + (2 + x) + (2 + x)/2

Now, let's simplify this expression:

Perimeter = x + 2 + x + (2 + x)/2

To add the fractions, we need a common denominator, which is 2:

Perimeter = x + 2 + x + (1/2)(2 + x)

Then, simplify further:

Perimeter = x + 2 + x + (1/2)(2) + (1/2)(x)

Perimeter = 2x + 2 + 1 + (1/2)x

Finally, combine like terms to express the perimeter in polynomial form:

Perimeter = (2x + 1/2x) + (2 + 1)

Perimeter = (2x + 0.5x) + 3.

To express the perimeter of the triangle in polynomial form, we first need to find the lengths of all three sides of the triangle.

Let's assume:
- The shortest side = x
- The longest side = x + 2 (since it is 2 more than the shortest side)
- The third side = (1/2)(x + x + 2) = (1/2)(2x + 2) = x + 1 (half of the sum of the longest side)

Now, we can calculate the perimeter by adding all three sides:
Perimeter = shortest side + longest side + third side
Perimeter = x + (x + 2) + (x + 1)
Perimeter = 3x + 3

Hence, the polynomial expression for the perimeter of the triangle is 3x + 3.