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

Video Transcript

If quadrilateral 𝐴𝐵𝐶𝐷 is similar to quadrilateral 𝑋𝑌𝑍𝐿, 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 𝐵𝐶 is proportional to side length 𝑌𝑍.

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.