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Given that area of rectangle = 8x² - 45y² + 18xy
one of the side = 4x+15y. 
Let it be the length.
So we need to find breadth.

We know that area = length×breadth
⇒ 8x² - 45y² + 18xy = (4x+15y)× breadth
⇒ breadth = (8x² - 45y² + 18xy)/(4x+15y)
⇒ breadth = (2x-3y)(4x+15y)/(4x+15y)
⇒breadth = 2x - 3y

So adjacent side is (2x - 3y)