# Question Video: Identifying Algebraic Expressions Mathematics • 6th Grade

The side length of an equilateral triangle is 𝐿 and its perimeter is 𝑃. What is the mathematical relation between 𝑃 and 𝐿? [A] 𝑃 = 𝐿 + 3 [B] 𝑃 = 𝐿 − 3 [C] 𝑃 = 3𝐿 [D] 𝑃 = 1/3 𝐿. What is the term used to describe 𝐿 in 𝑃? [A] A variable [B] A constant

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### Video Transcript

The side length of an equilateral triangle is 𝐿 and its perimeter is 𝑃. What is the mathematical relation between 𝑃 and 𝐿? Is it (A) 𝑃 equals 𝐿 plus three. (B) 𝑃 equals 𝐿 minus three. (C) 𝑃 equals three 𝐿. Or (D) 𝑃 equals one-third 𝐿. What is the term used to describe 𝐿 in 𝑃? Is it (A) a variable or (B) a constant?

An equilateral triangle has three sides of equal length. In this question. We are told they’re of length 𝐿. The perimeter of any shape is the distance around the outside. This means that 𝑃 is equal to 𝐿 plus 𝐿 plus 𝐿. This simplifies to three 𝐿. We can calculate the perimeter of any equilateral triangle by multiplying its side length by three. The correct one of our answers is option (C) 𝑃 is equal to three 𝐿. We can use this equation to calculate the perimeter of any equilateral triangle when given the side length.

The second part of our question wants us to decide whether the term 𝐿 is a variable or a constant. A constant term will be one that never changes, for example, the positive three in option (A) and the negative three in option (B). A variable, on the other hand, will change or alter. As 𝐿 is the side length of the equilateral triangle, this will vary depending on the size of the triangle. And 𝐿 is therefore a variable. The correct answer is option (A). In the equation 𝑃 is equal to three 𝐿, 𝐿 is a variable and three is the coefficient of 𝐿.