Find the value of x.

The smaller triangle is similar to the larger triangle, which means corresponding sides occur in a fixed ratio. In particular, this means

2x/(x + 9) = (length of shortest leg in smaller triangle)/(2 times the same length)

since in the larger triangle, the shortest leg is twice as long as the shortest leg in the smaller triangle. (The ticks on the line segments mean they are congruent and have the same length.)

So

2x/(x + 9) = 1/2

4x = x + 9

3x = 9

x = 3

option 1

data plot with   3 dots over 33, 1 dot over 34, 2 dots over 35, no dot over 36, 1 dot over 37, 2 dots over 38, 4 dots over 39, and 2 dot over 40.