Question Video: Finding the Length of a Side in a Triangle given the Corresponding Side in a Similar Triangle and the Similarity Ratio between Them Mathematics • 8th Grade

Given that the triangles shown are similar, determine π₯.

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Video Transcript

Given that the triangles shown are similar, determine π₯.

If two polygons are similar, then their corresponding angles are congruent which means theyβre the exact same measure, and the measure of their corresponding sides are proportional.

In our diagram, we can see that angle πΆ and angle π are congruent. Angle π΄ and Angle πΏ are congruent. And then the remaining angles, Angle π΅ and Angle π, they are congruent. We know this based on the markings of the angles.

From the markings of the angles, we can also tell which sides are proportional. So side π΄πΆ is proportional to side πΏπ. And side π΄π΅ is proportional to πΏπ.

This means we can set up a proportion. So π΄πΆ is proportional to πΏπ, and π΄π΅ is proportional to πΏπ. So the sides on the numerators are from triangle π΄π΅πΆ, and the sides on the denominators are from triangle πΏππ. Now we can plug in our values. π΄πΆ is ten, πΏπ is π₯, π΄π΅ is nine, and πΏπ is sixteen. Now we will find the cross product to solve for π₯.

So now we have nine times π₯ equals ten times sixteen. Letβs multiply. So nine π₯ equals one hundred and sixty. Now divide both sides by nine, and π₯ is equal to one hundred and sixty ninths.

Therefore, πΏπ equals one hundred and sixty ninths.