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What kind of equation could I use to solve this/how do I solve this:

If the same length is cut off three pieces of wood measuring 21cm, 42cm, and 45cm, the three pieces of wood can be assembled into a right triangle. What length needs to be cut off each piece?



Answer :

suppose the length needed to cut off as x
set quadratic equations and use the pythagorean identity (21-x)^2+(42-X) ^2=(45-x)^2
expand and distribute both sides to get quadratic equation x^2-36x+180=0, and find x to be 6cm

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