Triangle ABC is similar to triangle DBE. AC : DE is 3:2 and the length of AB is 42. What is the length of DE
Need help ASAP

Explanation:

AC : DE = 3:2 is another way of saying AC/DE = 3/2

This same ratio can be applied to AB : DB, so,

AB : DB = 3:2 which is the same as AB/DB = 3/2

We're told that AB is 42, which allows us to find DB

AB/DB = 3/2

42/DB = 3/2

42*2 = DB*3 ... cross multiply

84 = 3DB

3DB = 84

DB = 84/3 dividing both sides by 3

Side note: There is not enough info to find the length of DE. We would need to know the length of AC.

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.