Question

Part A: The length of two sides of a triangle are:

Side 1:

Side 2:

The perimeter of the triangle is

Part A: What is the total length of the two sides, 1 and 2, of the triangle? Show your work. (7 points)

Part B: What is the length of the third side of the triangle? Show your work. (7 points)

Answer 1

Part A: The total length of the two sides, 1 and 2, of the triangle is 10x² + 14x - 8

Part B: The length of the third side of the triangle is 10x³ -2x²  - 16x + 2

Calculating the sides of a triangle

From the given information,

The length of side 1 is

6x² - 4x - 2

and the length of side 2 is

18x + 4x² - 6

Part A

The total length of the two sides, 1 and 2, of the triangle will be

Length of side 1 + Length of side 2

That is,

6x² - 4x - 2 + 18x + 4x² - 6

This becomes,

6x² + 4x² + 18x - 4x - 2   - 6

10x² + 14x - 8  

Therefore, the total length of the two sides, 1 and 2, of the triangle is 10x² + 14x - 8

Part B

The length of the third side will be

Perimeter of the triangle - the total length of sides 1 and 2

From the given information,

The perimeter of the triangle is 10x³ + 8x² - 2x - 6

Then,

Length of third side = 10x³ + 8x² - 2x - 6 - (10x² + 14x - 8)

Length of third side = 10x³ + 8x² - 2x - 6 - 10x² - 14x + 8

Length of third side = 10x³ + 8x² - 10x²  - 2x - 14x - 6  + 8

Length of third side = 10x³ -2x²  - 16x + 2

Hence, the length of the third side of the triangle is 10x³ -2x²  - 16x + 2

Learn more on Calculating the sides of a triangle here: https://brainly.com/question/12183930

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