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Kathryn Kingham

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

If quadrilateral π΄π΅πΆπ· is similar to quadrilateral ππππΏ, what is the length of side π΄π·?

To solve this problem, well remember that similar polygons have proportional side lengths; this means that the side length π΄π· will be proportional to the side length ππΏ. In the same way, the side length π΅πΆ is proportional to side length ππ.

π΄π· over 18 must be equal to 14 over 12. We can use cross-multiplication to solve this problem. π΄π· 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 π΄π·. 252 divided by 12 equals 21. Side length π΄π· is equal to 21, but 21 what? The distances here are measured in centimetres, which means π΄π· is equal to 21 centimetres.

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