Trevor and his friends are making a four-square court that will be 10 feet long and 10 feet wide. To protect spectators from the action, they will include a safety zone around the outside of the court that will be the same width around each edge.The total area of the court and safety zone together in square feet can be modeled by the expression (10+2x)(10+2x), where x is the width of the safety zone in feet. This expression can also be written in the form 4x2+40x+100.What does the quantity 4x2+40x represent in the expression?(A)the perimeter around the outside of the safety zone in feet(B)the area of the court in square feet(C)the length of the court and safety zone together in feet(D)the area of the safety zone in square feet
Q. Trevor and his friends are making a four-square court that will be 10 feet long and 10 feet wide. To protect spectators from the action, they will include a safety zone around the outside of the court that will be the same width around each edge.The total area of the court and safety zone together in square feet can be modeled by the expression (10+2x)(10+2x), where x is the width of the safety zone in feet. This expression can also be written in the form 4x2+40x+100.What does the quantity 4x2+40x represent in the expression?(A)the perimeter around the outside of the safety zone in feet(B)the area of the court in square feet(C)the length of the court and safety zone together in feet(D)the area of the safety zone in square feet
Total Area Expression: The expression for the total area is (10+2x)(10+2x), which expands to 4x2+40x+100.
Court Area: The term 100 represents the area of the court itself, which is 10 feet by 10 feet.
Corner Area: The term 4x2 represents the area of the four corners of the safety zone, each being x by x feet.
Side Area: The term 40x represents the area of the four sides of the safety zone, two being 10x feet and two being x(10+2x) feet, but since we're only looking for the linear part, it's just 10x for each of the four sides.
Total Safety Zone Area: So, 4x2+40x represents the total area of the safety zone around the court.
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