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Ed is planning to put a square fish pond in the corner of his backyard. He is also planning to add a 55-foot-wide walkway around two sides of the fish pond, since the backyard fence will go along the other two sides.\newlineThe total area of the fish pond and walkway in square feet can be modeled by the expression (x+5)(x+5)(x + 5)(x + 5), where xx is the width of the fish pond in feet. This expression can also be written in the form x2+10x+25x^2 + 10x + 25.\newlineWhat does the quantity 10x+2510x + 25 represent in the expression?\newline(A)the length of the fish pond and walkway together in feet\newline(B)the perimeter around the outside of the fish pond and walkway together in feet\newline(C)the area of the fish pond in square feet\newline(D)the area of the walkway in square feet

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Q. Ed is planning to put a square fish pond in the corner of his backyard. He is also planning to add a 55-foot-wide walkway around two sides of the fish pond, since the backyard fence will go along the other two sides.\newlineThe total area of the fish pond and walkway in square feet can be modeled by the expression (x+5)(x+5)(x + 5)(x + 5), where xx is the width of the fish pond in feet. This expression can also be written in the form x2+10x+25x^2 + 10x + 25.\newlineWhat does the quantity 10x+2510x + 25 represent in the expression?\newline(A)the length of the fish pond and walkway together in feet\newline(B)the perimeter around the outside of the fish pond and walkway together in feet\newline(C)the area of the fish pond in square feet\newline(D)the area of the walkway in square feet
  1. Total Area Expression: The expression for the total area is (x+5)(x+5)(x + 5)(x + 5), which is also written as x2+10x+25x^2 + 10x + 25.
  2. Fish Pond Area: The term x2x^2 represents the area of the fish pond itself, since the pond is square and each side is xx feet long.
  3. Walkway Area: The term 10x+2510x + 25 must then represent the additional area added by the walkway, since the total area includes both the pond and the walkway.
  4. Calculate Walkway Area: To find the area of the walkway, we can subtract the area of the pond x2x^2 from the total area x2+10x+25x^2 + 10x + 25, which leaves us with 10x+2510x + 25.
  5. Area of Rectangles: The term 10x10x represents the sum of the areas of two rectangles formed by the walkway on two sides of the pond, each with one side of length xx and the other side of length 55.
  6. Corner Square Area: The term 2525 represents the area of the square at the corner, which is the part of the walkway that wraps around the corner of the pond, with each side being 55 feet long.
  7. Final Walkway Area: Therefore, the quantity 10x+2510x + 25 represents the area of the walkway in square feet.

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