Each pair of polygons below is similar. find the value of x. some answers may be decimals.

The answer to your question is below.

Step-by-step explanation:

14.- Use proportions to solve these problems.

                               14(x + 6) = 10(x + 9)

                               14x + 84 = 10x + 90

                               14x - 10x = 90 - 84

                                         4x = 6

                                           x = 6/4

                                          x = 3/2

15.-        

                            10(x - 1) = 8(x + 2)

                            10x - 10 = 8x + 16

                            10x - 8x = 16 + 10

                                     2x = 26

                                       x = 26 / 2

                                      x = 13

16.-      

                            5(x + 1) = 9(10/3)

                            5x + 5 = 30            

                                  5x = 30 - 5

                                  5x = 25

                                    x = 25 / 5

                                    x = 5

i think it might be a but you might want a second opinion

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240