9
advanced-math

A square picture frame has a border of width 2 inches. If the inner picture has side length xx, what is the area of the entire frame (picture + border)?

A

x2+4x+4x^2 + 4x + 4

B

x2+8x+16x^2 + 8x + 16

C

x2+4x^2 + 4

D

x2+16x^2 + 16

Correct Answer: B

Choice B is the correct answer.

  1. The inner side is xx.
  2. The border adds 2 inches to the left and 2 inches to the right (or top/bottom). So the total side length is x+2+2=x+4x + 2 + 2 = x + 4.
  3. The area of the entire square is (x+4)2(x + 4)^2.
  4. Expand: x2+8x+16x^2 + 8x + 16.

Choice A is incorrect because it assumes the border is only on one side (x+2x+2). Choice C is incorrect because it forgets the middle term. Choice D is incorrect because it forgets the middle term.

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