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The answer to your question is 6.- x = 13  7.- Perimeter = 49

Step-by-step explanation:

6.- If the triangles are similar then their angles measure the same

             8x + 16 = 120

             8x = 120 - 16

             8x = 104

               x = 104/8

               x = 13

7.- Use proportions to find the length of the other sides

                                  AC = 11

                                            AC = 16

                             BC =

                                            BC = 22

  Find the perimeter

  Perimeter = AB + BC + AC

                    = 11 + 22 + 16

                   = 49

Step-by-step explanation:

6) ∆ ABC is similar to ∆ CDE. This means that

Angle B = angle D

Therefore,

8x + 16 = 120

Subtracting 16 from the left hand side and the right hand side of the equation, it becomes

8x + 16 - 16 = 120 - 16

8x = 104

Dividing the left hand side and the right hand side of the equation by 8, it becomes

8x/8 = 104/8

x = 13

7) ∆ ABC is similar to ∆ XYZ. It means that

AB/XY = BC/YZ = AC/XZ

Therefore

11/22 = AC/32

22AC = 32 × 11 = 352

AC = 352/22 = 16

The factor is 2

Therefore,

BC = 44/2 = 22

Perimeter of ∆ABC = 22 + 16 + 11 = 49

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.