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B. 16

Step-by-step explanation:

a2 x b2 = c2 (pythag theorem)

We have the longest value (hypotenuse) opposite of the 90 degree angle, so 20 is C. 12 can be plugged in for either A or B

12^2 x b^2 = 20^2 (plug in for values)

144 x b^2 = 400 (simplify)

b^2 = 256 (subtract)

b = 16 (square root)

16

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.