Some triangles on the GRE are "special" right triangles-right triangles whose side lengths always come in predictable ratios. If you can spot them, you won't have to use the Pythagorean theorem to find a missing side length.
3:4:5 Right Triangles
These right triangles all have side lengths in the ratio 3:4:5. Be on the lookout for multiples. If you multiply 3, 4, and 5 each by the same number, you get a ratio equivalent to 3:4:5. For example, 6:8:10 is equivalent to 3:4:5 because 6, 8, and 10 are multiples of 3, 4, and 5 respectively, using the same multiplier, 2. So look for multiples-it will help you spot equivalent ratios.
5 : 12 : 13 Triangles
Right triangles whose sides are in the ratio 5: 12: 13 also occur frequently in GRE Quantitative Reasoning questions. You can verify that the three numbers 5, 12, and 13 form a Pythagorean triple by testing them in the Pythagorean theorem. If a = 5, b = 12, and c=13, does a2+b2=c2 ?
Yes, it does
52 + 122 = 132
25 + 144 = 169
169 = 169
Keeping an eye out for the side lengths 5, 12, and 13-or multiples of those numbers can help you apply your reasoning skills to a problem with one of these special triangles.
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