# Thread: [SOLVED] Simple Co-Ordinate Geometry

1. ## [SOLVED] Simple Co-Ordinate Geometry

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?

Thanks.

2. Hello unstopabl3
Originally Posted by unstopabl3

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?

Thanks.
You don't tell us where the point C is, but I think you want an explanation of why:
$\displaystyle \tfrac12\sqrt{52}\sqrt{13} = 13$
I think you have explained it perfectly well (although I don't really understand your use of the word 'under').
$\displaystyle \sqrt{52}=\sqrt{4\times13} = \sqrt4\times\sqrt{13} = 2\sqrt{13}$
Hence:
$\displaystyle \tfrac12\sqrt{52}\sqrt{13}= \tfrac12\times2\sqrt{13}\sqrt{13} = 13$
I can't explain why you got $\displaystyle 5.41$ on a calculator. Do it again. The answer is $\displaystyle 13$.

When do you rationalise and when do you use a calculator? The answer is that you should attempt to rationalise every time - only reaching for a calculator as a last resort!