Select the three measurements that could be side lengths that form a right triangle
7cm
11cm
54 cm
60 cm
61 cm
65 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.                  

simplified/solved

anwser:

-80x^2+158x+158