when preparing the operating activities section of the statement of cash flows using the indirect method

We know, perimeter = 2(l + w)
So, 2(l + w) = 30
2l + 2w = 30
Divide the equation 2, 
l + w = 15

Now, Area = l * w
l * w = 54

Substitute the value of l from previous equation, 
(15-w) * w = 54
15w - w² = 54
w² - 15w + 54 = 0
w² - 6w - 9w + 54 = 0
w(w - 6) -9(w - 6) = 0
(w-6)(w-9) = 0
w = 6 or 9

In short, Your Dimensions would be: 6 × 9 in

Hope this helps!