A total of 2 squares each have side length r . A total of 6 equilateral triangles each have side

Question

A total of 2 squares each have side length r . A total of 6 equilateral triangles each have side length t . None of these squares and triangles shares a side. The sum of the perimeters of all these squares and triangles is 210 . Which equation represents this situation?

Accepted Answer

Choice C is correct. It&rsquo;s given that a total of 2 squares each have side length r . Therefore, each of the squares has perimeter 4 r . Since there are a total of 2 squares, the sum of the perimeters of these squares is 4 r + 4 r , which is equivalent to 2 4 r , or 8 r . It&rsquo;s also given that a total of 6 equilateral triangles each have side length t . Therefore, each of the equilateral triangles has perimeter 3 t . Since there are a total of 6 equilateral triangles, the sum of the perimeters of these triangles is 3 t + 3 t + 3 t + 3 t + 3 t + 3 t , which is equivalent to 6 3 t , or 18 t . Since the sum of the perimeters of the squares is 8 r and the sum of the perimeters of the triangles is 18 t , the sum of the perimeters of all these squares and triangles is 8 r + 18 t . It&rsquo;s given that the sum of the perimeters of all these squares and triangles is 210 . Therefore, the equation 8 r + 18 t = 210 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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