Top 7 Triangle Tricks, Part 6 of 7
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: 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 
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:
You can use the properties of a 45º: 45º: 90º triangle to find the diagonal of the square:
Use this property to solve a question on your own:
Answer:
Squares: (B)
The diagonal of any square is its side length times because the diagonal is the hypotenuse of two 45: 45: 90 triangles. Since the side of the square is 3, the diagonal is 3.
Read other articles in this series:
- Top 7 Triangle Tricks, Part 1 of 7: Similar Triangles are Often Hidden
- Top 7 Triangle Tricks, Part 2 of 7: The height of a triangle may be found outside of the triangle itself
- Top 7 Triangle Tricks, Part 3 of 7: Certain integers that satisfy the Pythagorean Theorem are often used as the lengths of triangle legs
- Top 7 Triangle Tricks, Part 4 of 7: Any right triangle with a hypotenuse twice as long as one of the sides is a 30º: 60º: 90º triangle
- Top 7 Triangle Tricks, Part 5 of 7: An equilateral triangle has two internal 30º: 60º: 90º triangles
- Top 7 Triangle Tricks, Part 6 of 7: The length of a square’s diagonal is the side length multiplied by square root of 2
- Top 7 Triangle Tricks, Part 7 of 7: When a square is inscribed in a circle, the diameter of the circle is also the diagonal of the square
4 comments
Leon1984 on October 25th, 2009 at 4:57 am
"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?
Monther Jordan on October 25th, 2009 at 11:46 am
I didt see your comment as I made the same point
Monther Jordan on October 25th, 2009 at 11:45 am
There is an error in the first example as the hypotenuse lenght should be "5 square root of 2" not "10"
Eric Bahn on October 26th, 2009 at 4:40 pm
Error has been fixed, thanks!