This a question about perimeter and equation, let's see how to solve that:
The perimeter of a rectangle is the sum of its 4 sides. In this case, we know that the perimeter is 118. We can do an equation with these datas:
[tex]\boxed{AB + BC + CD + DA = 118}[/tex]
We also know other informations: the side AB is equal to [tex]4y+3[/tex] and de side BC is equal to 3y. In a recltangle, parallels sides have the same value. So, the side CD is equal to [tex]4y+3[/tex] and the side DA is equal to 3y.
Now, we have these datas:
[tex]AB + BC + CD + DA = 118\\\\AB = CD = 4y + 3\\BC = DA = 3y[/tex]
Let's do and solve an equation:
[tex]AB + BC + CD + DA = 118\\\\4y+3 + 3y + 4y+3 + 3y = 118\\14y + 6 = 118\\14y = 118 - 6\\14y = 112\\y = \frac{112}{14} \\y = 8[/tex]
So, the value of y is 8. Let's replace the value of y in the side AB:
[tex]4y + 3\\4\times 8 + 3 = 35[/tex]
Therefore, the length of side AB is 35.
