The length of side RS is 23.8 units.
The image shows a triangle, NOP, similar to triangle QRS. The length of NO is 10, NP is 7, and QS is 34. We are asked to find the measure of side RS.
Since the triangles are similar, we know that the corresponding sides are proportional. This means that we can set up a proportion to find the length of RS.
NO : NP = QR : RS
Substituting in the values we know, we get:
10 : 7 = 34 : RS
Multiplying both sides by RS, we get:
10RS = 34 * 7
Dividing both sides by 10, we get:
RS = 34 * 7 / 10
Calculating the answer, we get:
RS = 23.8
Therefore, the length of side RS is **23.8 units**, rounded to the nearest tenth.