Strategies, Sample Questions, and Random Ramblings.

by ejkiv

July 19, 2015

GMAT Right triangles are everywhere on the exam. Make sure you spend some good time studying the portions of this chapter so that you can easily move between the rules, and you do not have to spend too much time recalling the relationships. There are two components to GMAT right triangles:

**Hypotenuse:** The longest side, which is also opposite the right angle.

**Legs:** The two sides that meet to form the right triangle.

For the area of the right triangle the legs make up the base and height.

You can also use what is known as the Pythagorean Theorem to calculate the lengths of the sides of a right triangle.

**Pythagorean Theorem:** a^2 + b^2 = c^2 where ‘a’ and ‘b’ are the legs of the right triangle and ‘c’ is the hypotenuse.

All you are going to have to do on the exam with this formula is plug in the numbers, follow the order of operations and reduce the radicals as discussed in the chapters on calculations and roots, respectively.

Before you go through the calculations just discussed, however, you should always check for ‘special triangles.‘ These come in a few different forms:

**Pythagorean Triples:** Specific triangles that have all sides with integer lengths.

**30:60:90 Triangles:** Triangles with angle measures of 30, 60 and 90 degrees.

**45:45:90 Triangles:** Triangles with angle measures of 45, 45 and 90 degrees.

First Pythagorean Triples. There are 3 Pythagorean triples that you will need to remember: 3:4:5, 5:12:13, and 7:24:25. The first two numbers in each of these scenarios represent the legs of the triangles and the third represents the hypotenuse. Thus, they look like this:

These triples also exist in multiples of the value in the previous diagram. Basically, 3:4:5 is simply a ratio for the sides. Whereas, 3:4:5 triangles can also be represented as 6:8:10, 9:12:15, and so on. Make sure you test the multiples and the original triples before you dive into the math - remember keep it simple.

After that, you have 30:60:90 and 45:45:90 triangles. The ratio of the sides for these triangles are as follows:

**30:60:90 -** x : x(sqrt(3)) : 2x - where the value represented is the length of the side opposite its respective angle

**45:45:90 -** x : x : x(sqrt(2)) - where the value represented is the length of the side opposite its respective angle

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