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