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Four triangles are to be cut and removed from a square piece of sheet metal to create an octagonal sign with eight equal sides, as shown in the figure above. If the total area of the removed material is 196 square centimeters, what is the perimeter, in centimeters, of the octagon?
    Correct answer is '112'. Can you explain this answer?
    Most Upvoted Answer
    Four triangles are to be cut and removed from a square piece of sheet ...
    Notice that the “cutouts” can be reassembled to form two squares with side x and diagonal y, leaving an octagon with perimeter 8y.

    Since each of the cutout triangles is a right triangle: x2 + x2 = y2
    Simplify: 2x2 = y2
    If the total area of the “cutouts”
    is 196 square centimeters: 2x2 = 196
    Substitute 2x2 = y2 : y2 = 196
    Take square root: y = 14
    Therefore the perimeter of the octagon is 8 x 14 = 112.
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    Four triangles are to be cut and removed from a square piece of sheet metal to create an octagonal sign with eight equal sides, as shown in the figure above. If the total area of the removed material is 196 square centimeters, what is the perimeter, in centimeters, of the octagon?Correct answer is '112'. Can you explain this answer?
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    Four triangles are to be cut and removed from a square piece of sheet metal to create an octagonal sign with eight equal sides, as shown in the figure above. If the total area of the removed material is 196 square centimeters, what is the perimeter, in centimeters, of the octagon?Correct answer is '112'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about Four triangles are to be cut and removed from a square piece of sheet metal to create an octagonal sign with eight equal sides, as shown in the figure above. If the total area of the removed material is 196 square centimeters, what is the perimeter, in centimeters, of the octagon?Correct answer is '112'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four triangles are to be cut and removed from a square piece of sheet metal to create an octagonal sign with eight equal sides, as shown in the figure above. If the total area of the removed material is 196 square centimeters, what is the perimeter, in centimeters, of the octagon?Correct answer is '112'. Can you explain this answer?.
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