if the length of Q is 25% more than the length of P, this means it is 25% more than 40.
25% of 40 is 40÷4 which is 10
add this to 40 which means the length of Q is 50cm.
you can also do this by doing 40 × 1.25
now you know the area of Q is 10% less than the area of P.
first you need to make 2 equations for the area of each shape.
Area of P = length × width
= 40x
Area of Q = length × width
= 50y
now you need to find 10% of the Area of P
this means you need to find 10% of 40x which is 4x
subtract 4x from 40 as its 10% less
= 36x
(you can also do this by doing 40x × 0.9)
so 50y = 36x
swap this around so x is on the left
36x : 50y
then remove the x and y
36:50
simplify by dividing by 2
18:25
ratio of x:y is 18:25
I think this is how you do it but I'm not certain so I'm sorry if its wrong