A gardener is planting two types of trees:
Type A is 10 feet tall and grows at a rate of 21 inches per year.
Type B is 7 feet tall and grows at a rate of 25 inches per year.
Algebraically determine exactly how many years it will take for these trees to be the
same height.

9 years will take foe these trees to be the same height, If type A is 10 feet tall and grows at a rate of 21 inches per year and type B is 7 feet tall and grows at a rate of 25 inches per year.

Step-by-step explanation:

The given is,

                Type A is 10 feet tall and grows at a rate of 21 inches per year

                Type B is 7 feet tall and grows at a rate of 25 inches per year

Step:1

             Convert the rate of grows of tree inch to feet,

             For Tree A,

                   Rate of grow, A = 21 inches per year

                                              = 21 × 0.0833333      ( 1 inch = 0.0833333 feet)

                                             = 1.75 feet per year

              For Tree B,

                   Rate of grow, B = 25 inches per year

                                              = 25 × 0.0833333     ( 1 inch = 0.0833333 feet)

                                             = 2.08333 feet per year

Step:2

           Difference in the tall of  Tree A & B,

                                               = 10 - 7

                                              = 3 feet

           Difference in the rate of grow of tree A & B,

                                                = 2.08333 - 1.75

                                               = 0.3333325 feet per year

Step:3

           Year take to both trees are same height,

                                               = 9 years

Step:4

            Check for solution,

            Height of tree = Height of Tree + (Rate of grow × Years)

            For A,

                                    = 10 + ( 1.75 × 9 )

                                   = 25.75 feet.........................................(1)

            For B,

                                   = 7 + ( 2.08333 × 9 )

                                    = 25.74999

                                   ≅ 25.75 feet.....................................(2)

          From Equation (1) and (2),

                  25.75 feet = 25.75 feet

Result:

          9 years will take foe these trees to be the same height, If type A is 10 feet tall and grows at a rate of 21 inches per year and type B is 7 feet tall and grows at a rate of 25 inches per year.

ca = ec

cpctc makes it so that corresponding parts of the triangle you proved to be equal are equal, the other options aren't part of the part of the triangles you proved to be equal.