A rectangular photograph is surrounded by a border that is 1 inch wide on each side.
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 6 inches wide on each side, the total area would have been (M + 200) square inches. What is the perimeter of the photograph, in inches?
Answer/Solution
12
Steps/Work
Let x and y be the width and length of the photograph.
(x+2)(y+2)=M and so (1) xy + 2x + 2y + 4 = M
(x+12)(y+12)=M and so (2) xy + 12x + 12y + 144 = M+200
Let's subtract equation (1) from equation (2).
10x + 10y + 140 = 200
2x + 2y = 12, which is the perimeter of the photograph.
The answer is B.
(x+2)(y+2)=M and so (1) xy + 2x + 2y + 4 = M
(x+12)(y+12)=M and so (2) xy + 12x + 12y + 144 = M+200
Let's subtract equation (1) from equation (2).
10x + 10y + 140 = 200
2x + 2y = 12, which is the perimeter of the photograph.
The answer is B.