Find the value of xxx in the triangle shown below. Choose 1 Choose 1 (Choice A) A x=\sqrt{21}x= 21 x, equals, square root of, 21, end square root (Choice B) B x=\sqrt{42}x= 42 x, equals, square root of, 42, end square root (Choice C) C x= 15x=15x, equals, 15 (Choice D) D x=21x=21

x = 15.8114

Step-by-step explanation:

The complete question is:

"The problem is asking for value of x. Two right triangles side by side, the altitude is 9. The bottom of whole triangle is 25. One side is 15 and the other side is x. What is the value of x?"

Solution:-

- Develop a diagram for the information given " Two right triangles side by side" The altitude i.e height (common to both triangle ) = 9. The total base length of both triangles is = 25. One side is 15 and other side is x.

                                x

                             x x  x

                           x   x    x

                         x     x       x  

                       x       x          x       x = ?

                     x         x             x

           15     x          x                x

                 x             x   9              x

               x               x                      x

             x                 x                         x

           x                   x                            x

         x                     x                               x

       x                       x                                  x

  B  x x x x x x x x x x x x x x x x x x x x x x x  C

                  y           D                  25-y

- We will first determine the value of "y" using the left hand side triangle and apply pythagorean theorem. Where, H = 15 , P = 9 , B = y.

                                H^2 = P^2 + B^2

                                15^2 = 9^2 + y^2

                                y = √(225 - 81 )

                                y = 12

- Now we can use the value of y and apply pythagorean theorem on right hand side triangle with sides. H = x , P = 9 , B = 25-y = 25 - 12 = 13.

                               H^2 = P^2 + B^2

                               x^2 = 9^2 + 13^2

                               x = √( 81 + 169 )

                               x = 15.8114

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