# Question Video: Finding the Perimeter of a Triangle with Sides Given as Algebraic Expressions Mathematics • 11th Grade

In the figure, find the values of π₯ and π¦.

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### Video Transcript

In the figure, find the values of π₯ and π¦.

In this question, we have a triangle π΄π΅πΆ. And the lengths of the sides are given either as numerical values or as algebraic expressions. We need to work out what the values of π₯ and π¦ are. But letβs begin by figuring out what type of triangle π΄π΅πΆ is. Weβre given that this angle π΅π΄πΆ is 60 degrees and the other angle π΄πΆπ΅ is also 60 degrees.

We may be able at this point to work out what the angle π΄π΅πΆ is, but letβs step through it. We can remember that the angles in a triangle add up to 180 degrees. So we could work out angle π΄π΅πΆ by having 180 degrees subtract 60 degrees subtract 60 degrees, which leaves us with 60 degrees. So now we have a triangle that has three equal interior angles. This means that we can say that triangle π΄π΅πΆ is an equilateral triangle.

Importantly for us, we now know that this means that all sides in the triangle will be the same length. We could therefore say that π΄π΅ is equal to π΄πΆ, which means that π₯ plus six must be equal to 26. We could now solve this to find the value of π₯. Subtracting six from both sides of this equation would give us that π₯ is equal to 20. So now weβve found our first value.

Letβs see if we can set up a similar equation to find the value of π¦. We can write that π΅πΆ is equal to the length π΄πΆ. Itβs also of course equal to π΄π΅ as well. π΅πΆ is of length π¦ plus three, and π΄πΆ is of length 26. So we can set these equal and solve to find π¦. This time, weβll subtract three from both sides, to give us that π¦ must be equal to 23. We could then give our answers to the question that π₯ is equal to 20 and π¦ is equal to 23.