Question a-tota
A total of squares each have side length . A total of equilateral triangles each have side length . None of these squares and triangles shares a side. The sum of the perimeters of all these squares and triangles is . Which equation represents this situation?
A total of 2 squares each have side length r . A total of 6 equilateral
Hard-difficulty · SAT Math · Linear Equations in Two Variables — Writing equations from data/points. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
Choice C is correct. It’s given that a total of squares each have side length . Therefore, each of the squares has perimeter . Since there are a total of squares, the sum of the perimeters of these squares is , which is equivalent to , or . It’s also given that a total of equilateral triangles each have side length . Therefore, each of the equilateral triangles has perimeter . Since there are a total of equilateral triangles, the sum of the perimeters of these triangles is , which is equivalent to , or . Since the sum of the perimeters of the squares is and the sum of the perimeters of the triangles is , the sum of the perimeters of all these squares and triangles is . It’s given that the sum of the perimeters of all these squares and triangles is . Therefore, the equation represents this situation.
Choice A is incorrect and may result from conceptual or calculation errors.
Choice B is incorrect and may result from conceptual or calculation errors.
Choice D is incorrect and may result from conceptual or calculation errors.
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