The lengths of two sides of a triangle are shown below:

Side 1: 8x^2 - 5x - 2

Side 2: 7x - x^2 + 3

The perimeter of the triangle is 4x^3 - 3x^2 + 2x - 6

Answer the following questions:

Part A: What is the total length of the two sides, 1 and 2, of the triangle?

Part B: What is the length of the third side of the triangle?

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

Question

Carleigh

Mathematics

13 July, 21:08

The lengths of two sides of a triangle are shown below:

Side 1: 8x^2 - 5x - 2

Side 2: 7x - x^2 + 3

The perimeter of the triangle is 4x^3 - 3x^2 + 2x - 6

Answer the following questions:

Part A: What is the total length of the two sides, 1 and 2, of the triangle?

Part B: What is the length of the third side of the triangle?

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

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Answers (1)

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Martin Smith · Answer 1

We are given the sides of the triangle equal to 8x^2 - 5x - 2 and 7x - x^2 + 3. The sum of the two lengths is just the total of the terms given. The sum is equal to 7x^2 + 12x + 1. The perimeter is the sum of all three sides, hence the third side is 4x^3 - 3x^2 + 2x - 6 - (7x^2 + 12x + 1) equal to 4x^3 - 10x^2 - 10x - 7. The operations used are just subtraction and addition.