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Anna would like to surround an 8 in 
×10 in photograph with a border of uniform width. Let 
x be the width of the border, in inches. Which of the following functions could she use to determine the area, 
A, in square inches 
(in^(2)), of the picture and border combined?
Choose 1 answer:
(A) 
A=(8-x)(10-x)
(B) 
A=(8-2x)(10-2x)
(c) 
A=(8+x)(10+x)
(D) 
A=(8+2x)(10+2x)

Anna would like to surround an 88 in ×10 \times 10 in photograph with a border of uniform width. Let x x be the width of the border, in inches. Which of the following functions could she use to determine the area, A A , in square inches (in2) \left(\mathrm{in}^{2}\right) , of the picture and border combined?\newlineChoose 11 answer:\newline(A) A=(8x)(10x) A=(8-x)(10-x) \newline(B) A=(82x)(102x) A=(8-2 x)(10-2 x) \newline(C) A=(8+x)(10+x) A=(8+x)(10+x) \newline(D) A=(8+2x)(10+2x) A=(8+2 x)(10+2 x)

Full solution

Q. Anna would like to surround an 88 in ×10 \times 10 in photograph with a border of uniform width. Let x x be the width of the border, in inches. Which of the following functions could she use to determine the area, A A , in square inches (in2) \left(\mathrm{in}^{2}\right) , of the picture and border combined?\newlineChoose 11 answer:\newline(A) A=(8x)(10x) A=(8-x)(10-x) \newline(B) A=(82x)(102x) A=(8-2 x)(10-2 x) \newline(C) A=(8+x)(10+x) A=(8+x)(10+x) \newline(D) A=(8+2x)(10+2x) A=(8+2 x)(10+2 x)
  1. Add border width to photograph: To find the area of the picture and border combined, we need to add the width of the border to each side of the photograph. The photograph is 88 inches by 1010 inches, so we will add xx inches to each side.
  2. Calculate new length with border: The new length of the photograph including the border will be the original length (88 inches) plus two times the border width (since the border is on both sides), which is 8+2x8 + 2x inches.
  3. Calculate new width with border: Similarly, the new width of the photograph including the border will be the original width (1010 inches) plus two times the border width, which is 10+2x10 + 2x inches.
  4. Find area of photograph and border: The area of the photograph and border combined, AA, can be found by multiplying the new length by the new width. \newlineA=(8+2x)(10+2x)A = (8 + 2x)(10 + 2x) \newlineTherefore, the correct option is (D) A=(8+2x)(10+2x)A=(8+2x)(10+2x).

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