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stepan [7]
3 years ago
11

HELPP PLEASEEE

Mathematics
1 answer:
MrRa [10]3 years ago
8 0

Answer: The answer to your question is 6\sqrt{3}

Step-by-step explanation:

To solve this problem we will use proportions. We will compare the largest right triangle and the medium size triangle.

                          Medium triangle                     Large triangle

hypotenuse                 y                                            9 + 3

adjacent size               9                                               y

- Write the proportions

                                  y/9 = (9 + 3)/y

-Solve for y

                                  y² = 9(12)

                                  y² = 108

                                  y =   \sqrt{180}

-Find the prime factors of 108

                                  108  2

54 2

                                     27 3

                                      9  3

                                      3   3

                                       1

then,       108 = 2² 3³

-Expressthe root as fractional exponents

                                  2²/² 3²/² 3¹/²

-Simplification

                                   2(3)(3)¹/²

-Result

                                      6\sqrt{3}

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