The Pythagoras theorem
Last updated: 15 Nov 2008
If you have a right angled triangle with sides of length a, b and c then the Pythagoras theorem tells us
For this formula to work side c must be the hypotenuse which is the longest side. You can also identify the hypotenuse because it is opposite the right angle.
This is one of the most important formulas that you will learn for the GMAT, it is also one of the formulas that people make the most mistakes with so be careful. When we do some examples with Pythagoras we will see some of the most common mistakes made.
A Note on Square Roots
You will need to know about simplifying square roots if you are to use the Pythagoras theorem successfully in the GMAT.
Basically if you are taking the square root of a number which has a factor which is a perfect square (like 4, 9, 16, 25....) then you can take the factor out of the square root.
For example, if you have a right angled triangle with short sides 4 and 2 what is the length of the hypotenuse?
To solve this you will use Pythagoras. Set c to be the length of the hypotenuse.
You will never find amongst the answers in a GMAT question because 4 is a factor of 20 and is also a perfect square and so we can simplify this square root.
...and this is the answer that you would find in a GMAT question.
Whenever you have a root in your answer you need to make sure that it is in its simplest form which means taking any factors which are perfect squares out of the root.
please help. The mathematical expressions are not loading very well. They just appear as 'Mathematical expression'. Thank you.
I am afraid this a problem with the site at the moment, I should have this fixed in about a week.
Pythagorus' correct spelling is Pythagoras.
How embarrassing. Thanks for the correction.