Question

A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 2 inches wide on each side, the total area would have been (M + 52) square inches. What is the perimeter of the photograph, in inches?

Answer 1

if 1 inch is added, you would add 2 inches to to each side of rectangle.  

You would have: W+2, and, L+2,  

Now let W+2 = x and, L+2 = y  

Total area =  x*y=M  

If 1 inch is added again, like above you add 2 inches to both sides, you would then have:

(x+2)(y+2)=M+52;  

xy+2x+2y+4=M+52;  

xy=M

2x+2y=48  

x+y=48/2=24  

Now solve :

W+2+ L+2=24  

W+L=20  

The perimeter is 2(W+L)=20*2 = 40 inches.