i cannot understand this!!

[mellow zephyr]

can anyone help with this? me and my friends tried it and cant get the right answer, please help if you can!!

[icy mortar]

this question is asking for the ratio of sizes between the shapes, notice how the top of the green shape is 4cm and the top of the purple is 3cm, this gives a ratio of 4/3, the same ratio holds for the right side, as 12/9 is equal to 4/3. all we need to do now that we know the ratio is divide 7 by 4/3, this gives us 5.25cm, meaning w = 5.25