How do we know what to take as the base and height in triangles while solving? for eg, greg mentions here that in the smaller triangle, y is the base. and it’s different in the bigger triangle…how do i know for other problems?
The height is always perpendicular to the base. Also one triangle can have multiple bases with their corresponding heights - which one to use will depend on the problem.
how do i prevent myself from choose the wrong base? wouldnt that make my entire calculation go haywire?
Multiplication is commutative, so if you interchange them it’s fine. Not sure if that was your question, but yeah as mentioned above you have to select a perpendicular height from the selected base
but what if all the 3 sides of the triangle are of different measure? then what do i consider as the base to get the right answer?
Then you have to guess the height for a corresponding base with the help of pythagorean triplets. Alternatively, you would find the area of the triangle with heron’s and then solve for the height by using A = \frac 12 bh.