Question

PLZ HELP
The lengths of two sides of a triangle are shown.

Side 1: 3x2 − 4x − 1

Side 2: 4x − x2 + 5

The perimeter of the triangle is 5x3 − 2x2 + 3x − 8.

Part A: What is the total length of the two sides, 1 and 2, of the triangle? Show your work. (4 points)

Part B: What is the length of the third side of the triangle? Show your work. (4 points)

Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points)

Answer 1

perimeter of triangle is = s+s+s

so , 3x2-4x-1 + 4x-x2+5+ third side = 5x3-2x2+3x-8

Answer 2

Given ;

The lengths of the two sides of a triangle are shown.

Side 1: 3x2 − 4x − 1

Side 2: 4x − x2 + 5

The perimeter of the triangle is 5x3 − 2x2 + 3x − 8.

To Find; The length of the third side

Solution; It is given that The lengths of two sides of a triangle are shown.

Side 1: 3x2 − 4x − 1

Side 2: 4x − x2 + 5

The perimeter of the triangle is 5x3 − 2x2 + 3x − 8.

Let the third side be y

Perimeter = Sum of all sides

3x2 − 4x − 1+ 4x − x2 + 5+y=5x3 − 2x2 + 3x − 8.

2x2+4+y = 5x3 -2x2 +3x -8

y= 5x3-4x2+3x-12

Hence the third side is 5x3-4x2+3x-12