A rectangular photo frame has outer length (20) and breadth (16). After removing a uniform border, the inner area is (192). What is the border width?

Correct answer: (2)

Let the uniform border width be x units. Since the border is removed from both opposite sides in each direction, the inner length becomes 20-2x and the inner breadth becomes 16-2x. The given inner area therefore gives \\(20-2x)(16-2x)=192\\. The width must also be positive and less than 8.

Testing option A, x=2 gives inner dimensions 16 and 12, whose area is 16 times 12=192. Thus option A is correct. Algebraically, expansion gives 4x^2-72x+128=0, or x^2-18x+32=0, with roots 2 and 16. The root 16 is impossible because it would make the inner dimensions invalid, so the physical border width is 2 units.