u/Healthy-Section-9934

My kid (year 7) had this pop up on her Sparx homework. She asked for some help, so I:

1. used Pythagoras to get the whole base (no calculator allowed so kept it as sqrt(135))
2. used that to get an area of the big triangle
3. Subtracted the green triangle area to get the little white triangle’s area
4. Got the dotted line segment (y) of the white triangle from that
5. Bit of algebra to find y = sqrt(135) - 8

So, I got the answer from that (seemed a bit involved for year 7, but hey ho). Turns out they’ve not done Pythagoras at school yet. Is there some way to solve it without using Pythagoras?