TOUGH GUY wrote:

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?

A- 34

B- 36

C- 38

D- 40

E- 42

If X and Y are the length and width of the photograph respectively (excluding the border) then

(X + 2)(Y + 2) = M ( since border is 1 inch on each side)

XY + 2X + 2Y + 4 = M ---> A

Also,

(X + 4) (Y + 4) = M + 52 (if border is 2 inch wide on each side)

XY + 4X + 4Y + 16 = 52 ---> B

Subtract A from B

2X + 2Y + 12 = 52

2X + 2Y = 40

2X + 2Y = Perimeter of photograph

So, D.