Triangles come up on the GMAT quite a bit. They can be quite complicated and difficult, but if you know the common patterns you can learn to navigate through these questions much more quickly.
Common Right Triangles:
There are several common right triangles that show up on the GMAT often. If you memorize these, you can spot them easily and avoid having to use the pythagorean theorem, which can be quite time consuming. These common right triangles include:
- (3:4:5), (6:8:10), (9:12:15)…
This means that if you are presented with a right triangle with a hypotenuse of 5 and one of the sides is 4, you know that the third side must be 3. This will be true for any other right triangle that has two sides that correspond to any of these patterns.
Isosceles Right Triangles:
The ratio of the sides for every isosceles right triangle is:
x : x : x√(2)
corresponding to the 45:45:90 degree angles respectively.
This means that whenever you have an isosceles right triangle, if you know the values for one of the sides and if it is the hypotenuse or not, you know the value of all of the sides. It also means that if you know the perimeter of the triangle, you can figure out the value of each side. You can also figure out the sides from the area, which will be (b*h)/2 or (x2)/2. (x being the value of a side corresponding to a 45 degree angle).
A 30-60-90 triangle is a right triangle, but you can also think of it as one half of an equilateral triangle. The sides corresponding to the 30:60:90 degrees respectively are in the ratio:
x : x√(3) : 2x
That means, that you can also determine each side if you know the perimeter. You can also determine all other sides if you know one side and what angle it corresponds to. Unlike isosceles triangles, however, you cannot determine what the side values are simply from the area.
Knowing these GMAT triangle tricks will help you get through triangle problems mush more quickly and efficiently. Thus, it could be valuable for you to take the time to memorize these important right triangle facts, because they will save you a lot of time on test day.