2x-5y=17 ..solve for y

Height of support Y =  13.3333333 m, or if you want to round, ≅ 13.3 m. Height of support X = 10.6666667 m, or if you want to round, ≅ 10.7 m.

Step-by-step explanation:

This problem is looking at similar triangles. If you look closely, the three different supports form three different triangles. So, we are just dilating from the biggest triangle to the two smaller triangles!

We are given the base lengths for all the triangles, so let's start with finding the height of support Y. The biggest triangle's base length is 18 m, and Y's base length is 15 m. What we want to do is figure out the scale factor that would shrink the biggest triangle down to triangle Y. Aka, we divide 18 by 15.

18/15=1.2

Now, we can take the biggest triangle's height, 16 m, and divide it by this scale factor of 1.2.

16/1.2=13.3333333

So, the height of support Y is 13.3333333 m, or if you want to round, 13.3 m.

We can repeat this same process to find the height of support X.

18/12=1.5

16/1.5=10.6666667

The height of support X is 10.6666667 m, or if you want to round, 10.7 m.

I hope this helped, and if I was correct, I'd appreciate if you marked my answer as Brainliest :)