Step-by-step explanation:
what is the problem here, what do you not understand ?
you do know fractions, and how to multiply and divide them ? because that would be a precondition for a teacher to give you such a problem to solve.
so, if you do know the handling of fractions, this is very basic and easy thing to solve.
let's get into it then :
2 similar triangles. that means all lengths of all lines in one triangle are the result of multiplying the corresponding lines in the other triangle by a constant factor.
that is the meaning of a scaling factor.
it is like on a map, where it says 1 unit on the map is that many units out there in reality.
your teacher was really nice to point out the right angles and even a second angle (37 degrees), so that we can immediately see, which side or line of one triangle corresponds to which side or line of the other.
when we imagine now to turn e.g. the smaller triangle so that it is oriented the same way as the larger one, we see that QS corresponds to LJ. and QR to LK. and RS to KJ.
so, we are going in the scaling process from left to right. that means we are starting with the larger triangle and turn it into the smaller triangle.
so, what (scaling) factor do I need to multiply with 15 to get 10 ?
it is the same factor to go also from 9 to 6 and from 12 to 8.
15×x = 10
x = 10/15 = 2/3
15 × 2/3 = 30/3 = 10
12 × 2/3 = 24/3 = 8
9 × 2/3 = 18/3 = 6
so, as you can see, 2/3 is the correct scaling factor.
