GRE Quantitative Concepts

a^2 + b^2 is greater than c^2

c is the longest side of the triangle

a^2 + b^2 is less than c^2

• c is the longest side
• 

100 + 289 is less than 441

a^2 + b^2 = c^2

c is the longest side



9 + 16 = 25

25 + 144 = 169

for any positive number x, there is a right triangle whose sides are 3x, 4x, and 5x

ie x=pi

3pi, 4pi, and 5pi

• 
• sides are x, x, and x√2

sides are x, x√3, and 2x

Greater

• 
• Area = (s^2 √3)/4