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)

Question

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)

Bytelearn · Accepted Answer

Problem Understanding: Understand the problem. The photograph has dimensions of 8 inches by 10 inches. A border of uniform width x is to be added around the photograph. We need to find the function that represents the area of the photograph and the border combined.Determining Dimensions: Determine the dimensions of the photograph with the border. The width of the border is added to all four sides of the photograph. Therefore, the new width will be the original width plus two times the border width, and the new length will be the original length plus two times the border width. This gives us the dimensions (8 + 2x) by (10 + 2x) for the photograph with the border.Writing the Area Function: Write the function for the area of the photograph with the border. The area of a rectangle is found by multiplying the length by the width. Therefore, the area of the photograph with the border is A = (8 + 2x)(10 + 2x).Matching the Function: Match the function with the given options. The function we found in Step 3 is A = (8 + 2x)(10 + 2x), which matches option (D).

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