Reposted Question

Let m be the distance the squares overlap on the long edges.

First, express the area of the region the squares don't overlap in terms of the variable. (You can probabally skip this part, I'm just struggling to find more ways to use the variable :/ )

Area=2(7*(7-m))

The 2 comes from there being two rectangles, 7 is the height and 7-m is the width.

Now express the length of the total idth in terms of the variable.

14-m

With no overlap, the width would be 14, but to find the width after overlaping you have to subtract the distance they overlap

14-m=10

Set it equal to 10

-m=-4

Sutract 14 from each side

m=4

Divide by -1

Now that we have the distance they overlap, plug it into the equation from the beginning to get the answer.

2(7*(7-4))

2(7*3)

2*21

The area the squares don't overlap is 42

This question is flawed....to see why....

If the squares overlapped to a width  of 10....it would mean that each square would have to contribute a  width of 10.....but.....the width of  each square is only 7, so this is impossible

Mathematically.....let  x  be the width of  each  of the unshaded rectangles

Then....the width of the overlap  must just be 7 - x   

And this equals 10

So

7 - x   = 10

-x  = 3

x  = -3        which is impossible

I don't see how this problem is flawed?

The numbers seem to work out.