Question

The length of a picture frame is 3 in. greater than the width. The perimeter is less than 52 in. How do you find the dimensions of the frame?

Answer 1

We can at once replace `L=W+3`

Explanation:

`P=2xxL+2xxW=2xx(W+3)+2xxW`
`P=2W+6+2W=4W+6`

Now since `P<52`, we get:
`4W+6<52` subtracting 6:
`4W<52->W<13`

Conclusion:
Width is less than 13 inches
Length is less than 16 inches

Note :
There could not be just any combination of
`L<16andW<13` as `L=W+3` still holds.
(so `L=15, W=10` is not allowed)