Question

a postcard has an area of 24 square inches. two enlargements of the postcard have areas of 54 square inches and 96 square inches. in each postcard the length is 1 and 1/2 times the width. what could be the dimensions of the postcard or the enlargements.

Answer 1

So,

The length is always 1.5 times the width.

l = 1.5w

lw = 24
lw = 54
lw = 96

Or, we could put it this way:
1.5w(w) = 24
1.5w(w) = 54
1.5w(w) = 96

So,
1.5w^2=24
1.5w^2=54
1.5w^2=96

Dividing both sides by 1.5, we get:
w^2 = 16
w^2 = 36
w^2 = 64

And solving for the only logical dimension, we get:
w = 4
w = 6
w = 8

And their corresponding lengths:
l = 1.5(4) = 6
l = 1.5(6) = 9
l = 1.5(8) = 12

So a few lengths could be:
(l,w)
(6,4)
(9,6)
(12,8)

Of course, there are infinite solutions.

Answer 2

4 and 6 is the original. The 54 inch one is 6 and 9. The 96 inch one is 8 and 12