Which set of measurements could represent the three sides of a triangle? O 2 cm, 3 cm, 6 cm
O 1 cm, 4 cm, 6 cm
O 8 cm, 9 cm, 10 cm
6 cm, 10 cm, 18 cm

The side lengths of a right triangle is 11cm, 60cm and 61cm, that could be selected from the given measurements.

Step-by-step explanation:

The measurements are,

                  7cm, 11cm, 54cm, 60cm, 61cm, 65cm

Step:1

                 To check the right angle triangle, Pythagorean theorem can be used.

                For a Pythagorean theorem,

                                     (1)

               The side values are lower than the hypotenuse,

                                                        (2)

               Where,

                         a,b - side values

                            c - Hypotenuse

               For right angle triangle,  c > a, b

               Alternative : 1

               Take, a = 7cm, b = 11cm

               From eqn (2),

                                                   =  = 13.04

              The above value is not equal to the any one of the values of ( 54cm. 60cm, 61cm, 65cm ), So its not an sides of right triangle.

               Alternative : 2

               Take, a = 7cm, b = 54cm

               From eqn (2),

                                                   =  = 54.45

              The above value is not equal to the any one of the values of (60cm, 61cm, 65cm ), So its not an sides of right triangle.

               Alternative : 3

               Take, a = 7cm, b = 60cm

               From eqn (2),

                                                   =  = 60.406

              The above value is not equal to the any one of the values of (61cm, 65cm ), So its not an sides of right triangle.

               Alternative : 4

               Take, a = 7cm, b = 61cm

               From eqn (2),

                                                   =  = 61.40

              The above value is not equal to the values of (65cm ), So its not an sides of right triangle.

                 Alternative : 5

               Take, a = 11cm, b = 54cm

               From eqn (2),

                                                   =  = 55.1089

              The above value is not equal to the any one of the values of (60cm, 61cm, 65cm ), So its not an sides of right triangle.      

                Alternative : 6

               Take, a = 11cm, b = 60cm

               From eqn (2),

                                                  =  = 61

              The above value is equal to the values of (61cm ), So its an sides of right triangle. The three sides are 11, 60 and 61.

Step:2

            Check for solution,

Result:

            The side lengths of a right triangle is 11cm, 60cm and 61cm, that could be selected from the given measurements.                

Step-by-step explanation: The side lengths of a right triangle is 11cm, 60cm and 61cm.

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0