What you must know about Pythagorean Theorem ? GRE Math

Pythagorean Theorem is one of the most important things you must know for GRE Quant. Simply; Pythagorean Theorem establishes the relationship between the 3 sides of a right triangle.

If  and  are the legs of a right triangle and  is the hypotenuse:

The theorem can be written as an equation relating the lengths of the sides ,  and  as:

You should try to remember some commonly used Pythagorean triplets i.e. the typical dimensions of right triangles that frequently occur in GRE.

Commonly asked Pythagorean Triplets on the GRE

Length	Width	Hypotenuse
3	4	5
4	3	5
6	8	10
8	6	10
5	12	13
12	5	13

Problems involving Pythagorean Theorem will often test you on other triangle properties and geometry concepts:

Example:

If the length of the hypotenuse of the triangle shown above is , what is the value of ?

Solution:

 is a right triangle with hypotenuse . We are also told that the length of  is . We can apply Pythagorean Theorem to relate the two sides and the hypotenuse. However this problem can be solved much more easily if you recall the common Pythagorean triplets i.e. ,  and . Therefore we can plug in these values to see if we get consistent results:

and

This implies that 

If you want to solve mathematically we can set up the equation as:

We can factorize the quadratic equation shown above:

This implies that either  or . Since length of a triangle cannot be negative, the right answer is