In the trapezium $ABCD$ , $AB$ is parallel to $CD$ and $O$ is the intersection of $AD$ and $BC$. The line $PS$ is drawn through $O$ in such a way that $PS$ is parallel to $DC$. If $AB = 20$ AND $CD = 30$,what is the length of $PS$ ?
First I searched for similar triangles. According to that I saw that triangle DPO and triangle ADB are similar. In the other side triangle APO and triangle ADC are similar. By equalizing the lengths OP according to the two ratios, finally I got $PS = 24$. Is it correct?
Yes, you got it.
First, the board requests that you offer as much detail as you can, including an image and what you've done so far.
In my solution, the 4 and 6 are numbers chosen to be in a 2:3 ratio, not absolute numbers. This must be the ratios of the triangles heights as you observed.
Once we have that, we use the line splitter theorem from geometry to show PS as 24.