The lengths of two sides of a triangle are shown.

side 1: 8x2 − 5x − 2

side 2: 7x − x2 + 3

the perimeter of the triangle is 4x3 − 3x2 + 2x − 6.

part b: what is the length of the third side of the triangle? show your work.

answer:

the perimeter of a shape is the total length of the side of the shape.

from the equation above, let say the length of the third side is y

(8x2 - 5x - 2) + (7x - x2 + 3) + y = 4x3 - 3x2 + 2x - 6

rearrange the equation and put like terms together, the we have

8x2 - x2 - 5x + 7x - 2 + 3 + y = 4x3 - 3x2 + 2x - 6

7x2 + 2x + 1 + y = 4x3 - 3x2 + 2x - 6

make y subject of formula;

y = 4x3 - 3x2 - 7x2 + 2x -2x - 6 - 1

y = 4x3 - 10x2 + 0 - 7

y = 4x3 - 10x2 - 7

the length of the third side is 4x3 - 10x2 - 7

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation:

853.3

step-by-step explanation: