Top 7 Triangle Tricks, Part 6 of 7

by on October 25th, 2009

Triangles are commonly tested on the GMAT because they present many shortcuts for the savvy test taker. The makers of the GMAT know that the average student will rely on formulas and calculations, losing valuable time and possibly making careless mistakes. However, students who consistently report high math scores know the following tips and tricks for saving time and attacking triangles.  This article is the sixth part of a seven-part series.

6. The length of a square’s diagonal is the side length multiplied by square root of 2.

Like the 30º: 60º: 90º triangles, 45º: 45º: 90º triangles have a special property that states that the lengths of the sides have a ratio of s: s: ssqrt{2}. Therefore, you can identify the side lengths of two sides given just one side length:

PowerScore_Triangle_Part6_1

Because this is a 45º: 45º: 90º, you can determine that the hypotenuse is 5sqrt{2} and the base is 5.

A square has four equal angles, all measuring 90º. But if you divide the triangle by a diagonal, there are two 45º: 45º: 90º triangles:

PowerScore_Triangle_Part6_2

You can use the properties of a 45º: 45º: 90º triangle to find the diagonal of the square:

PowerScore_Triangle_Part6_3

Use this property to solve a question on your own:

PowerScore_Triangle_Part6_4

Answer:

Squares: (B)

The diagonal of any square is its side length times sqrt{2} because the diagonal is the hypotenuse of two 45: 45: 90 triangles. Since the side of the square is 3, the diagonal is 3sqrt{2}.

Read other articles in this series:

4 comments

  • "Like the 30º: 60º: 90º triangles, 45º: 45º: 90º triangles have a special property that states that the lengths of the sides have a ratio of s: s: s. Therefore, you can identify the side lengths of two sides given just one side length:

    Because this is a 45º: 45º: 90º, you can determine that the hypotenuse is 10 and the base is 5."

    Why? Shouldn't the hypotenuse be 5rt2? Why 10?

    • I didt see your comment as I made the same point :-)

  • There is an error in the first example as the hypotenuse lenght should be "5 square root of 2" not "10"

  • Error has been fixed, thanks!

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