5 beetles out of 45 insects.
1:9 is the answer

I suppose that this question is about ratios.

When we have A elements of one type, for every B elements of another type.

The ratio between these elements is A:B

In this particular case, we have:

5 beetles out of 45 insects (the 5 beetles do not belong to the group of 45 insects, if that where the case, we would not get the value 1:9 seen in the question)

Then there are 5 beetles and 45 insects.

The ratio is 5:45

Now, whit those we can divide both numbers by the same number and the ratio will be the same, then if we divide both by 5, we get:

(5/5):(45/5)

1:9

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

answer: what statements

step-by-step explanation if you write the statements down then i could you.