# Question Video: Using Proportions in a Triangle to Calculate an Unknown Length Mathematics • 11th Grade

Find the value of π₯.

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### Video Transcript

Find the value of π₯.

We see from the figure that the lines π΄πΆ and π΄π΅ are transversals that intersect parallel lines π·πΈ and π΅πΆ. And we know that the two pairs of corresponding angles created by this intersection are equal. Thatβs angles π·πΈπ΄ and π΅πΆπ΄ and angles πΈπ·π΄ and πΆπ΅π΄. This being the case, we can say the triangles π΄π΅πΆ and π΄π·πΈ are similar triangles since they each have the common angle π΅π΄πΆ and their other two angles are also equal.

Now recall that when two triangles are similar, the ratios of the length of their corresponding sides are equal. In particular, π΄π· is to π΄π΅ as π·πΈ is to π΅πΆ. In other words, π΄π· over π΄π΅ is equal to π·πΈ over π΅πΆ. Now, we know that π΄π· is equal to 10 units. π΄π΅ is equal to 10 plus 11 units, thatβs π΄π· plus π·π΅. π·πΈ is equal to 10 units, and π΅πΆ is π₯. And so we have 10 over 10 plus 11 is equal to 10 over π₯. That is, 10 over 21 is equal to 10 over π₯.

Now, solving for π₯, we multiply through by 21π₯ and divide both sides by 10, and we have π₯ equal to 21. Hence, using the given diagram, we find that π₯ is equal to 21 units.