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The side length of a rhombus is 𝑥 and its perimeter is 𝑃.
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What is the mathematical relation between 𝑃 and 𝑥?
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Is it (A) 𝑃 equals 𝑥 plus four, (B) 𝑃 equals 𝑥 minus four, (C) 𝑃 equals four 𝑥, or (D) 𝑃 equals one-quarter of 𝑥?
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What term do we use to describe 𝑥 in 𝑃?
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Is it (A) a variable or (B) a constant?
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We are told in the question that we have a rhombus of side length 𝑥.
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All four sides of a rhombus are equal in length.
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Therefore, each side of the rhombus must be equal to 𝑥.
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We know that the perimeter of any shape is the distance around the outside.
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𝑃 is therefore equal to 𝑥 plus 𝑥 plus 𝑥 plus 𝑥.
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This simplifies to four 𝑥.
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The perimeter of any rhombus can be calculated by multiplying its side length by four.
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The correct answer is therefore option (C), 𝑃 is equal to four 𝑥.
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We could then use this equation to calculate the perimeter when given the side length of any rhombus.
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The second part of our question asks us to describe what type of term 𝑥 is.
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Is it a variable or a constant?
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A constant term would be one that never changes, for example, the positive four in option (A) or the negative four in option (B).
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The 𝑥, on the other hand, is a variable as its value can vary depending on the side length of the rhombus.
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As it is the length of a shape, it could take any positive value.
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In the equation 𝑃 equals four 𝑥, 𝑥 is a variable and four is the coefficient of 𝑥.