What type of research relies on the researcher's first-hand observations of participants in naturally occurring contexts?

Qualitative Research

Step-by-step explanation:

In this type of research there is focus to collect data which is non numerical. This type of research tries to ask questions that relate to why and how something occurs rather than how many times it occurs.

Case study is an example of qualitative research. Quantitative research depends on the mathematical formulations and relations to come to a conclusion while qualitative research does not.

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.