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Video: Finding a Side Length in a Polygon given the Corresponding Side Length in a Similar Polygon

Kathryn Kingham

If ABCD is similar to XYZL, what is the length of AD?<Figure>


Video Transcript

If quadrilateral 𝐴𝐡𝐢𝐷 is similar to quadrilateral π‘‹π‘Œπ‘πΏ, what is the length of side 𝐴𝐷?

To solve this problem, well remember that similar polygons have proportional side lengths; this means that the side length 𝐴𝐷 will be proportional to the side length 𝑋𝐿. In the same way, the side length 𝐡𝐢 is proportional to side length π‘Œπ‘.

𝐴𝐷 over 18 must be equal to 14 over 12. We can use cross-multiplication to solve this problem. 𝐴𝐷 times 12 must be equal to 18 times 14. 18 times 14 equals 252.

Now I need to divide both sides by 12 to isolate side length 𝐴𝐷. 252 divided by 12 equals 21. Side length 𝐴𝐷 is equal to 21, but 21 what? The distances here are measured in centimetres, which means 𝐴𝐷 is equal to 21 centimetres.