To find the area of triangle ABC I found out magnitudes of AB and CM then used the formula 1/2 x Base x Height as following:
1/2 x under root 52 x under root 13
The answer I get is 5.41 when solved with the calculator. But the correct answer is 13.
I know that to get 13 square units as an answer we have to rationalize under root 52 into 2 under root 13 and then solve like this:
1/2 x 2 (under root 13 ) x under root 13
Then we cancel out 1/2 with 2 and multiple under root 13 with under root 13 to get under root 13 square. Then square cancels the under root and we get 13.
What I want to know is that why is it like this? Why don't we get the same answer when solved directly through a canculator? How are we supposed to know whether to rationalize such numbers or to solve them with a calculator?