The scale of the map is missing. the actual distance from liberty to west quall is 72 miles, and it is 6 inches on the map. a) what is the scale of the map? b) foston is between liberty and west quall and is 4 inches from liberty on the map. how far is foston from west quall?

72:6

Scale: 72/6=12 --> 1: 12

4*12=foston from west quall 
48miles=foston from west quall

We know that the length (L) of the rectangle in question is 7mm longer than its width (W). Let's represent that as the following:
L=7+W

A rectangle's perimeter (the total sum of its sides) will be made my 2 sides representing the length  (2L) and 2 sides representing the width (2W).  We also know that this rectangle's perimeter is greater than 62. Since eventually we are solving for W, let's state all expressions in terms of W:
2L=2(7+W)
2(7+W)+2W>62
14+2W+2W>62
14+4W>62
4W>62-14
4W>48
W>48/4
W>12
If the rectangle's perimeter is greater than 62, then the width  will be greater than 12. Let's confirm this:
Perimeter=2L+2W
P=2(7+12)+2(12)
P=14+24+24
P=62
So we can see that if the perimeter is to surpass 62, W needs to be greater than 12 and L ( which is also 7+W) needs to be greater than 19.