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.

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

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.