An architect wants to build three similar triangles such that the ratio of the middle triangle. The smallest one has side lengths 5, 12, and 13; the largest triangle has the side lengths 45, 108, and 117. If two of the middle triangle's sides are 39 and 36, what is the length of the third side?

 15

Step-by-step explanation:

small:     5     12      13

middle:  __   36     39

large:    45   108    117

Notice that to get from the small to the large, multiplied by 9

5(9) = 45    12(9) = 108    13(9) = 117

That is because the sides are proportional

To get from small to middle, multiply by 3  

5(3) = 15     12(3) = 36    13(3) = 39

To solve it using proportions:

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

pooopoopopoopop

step-by-step explanati∵∵∴∴on: