The older students become, the more there is a need for speed of solving simple problems. The exams do not have much time to solve simple examples or problems for a long time. How to find the diagonal of a square quickly and easily? This is where children begin to be taught from the eighth grade. This article provides two methods - one longer, the other faster.
How to calculate the diagonal of a square?
The first method is the already well-known and familiar Pythagorean theorem. In the square, all angles are right, which means that the diagonal divides it into two equal right triangles and is itself their hypotenuse. By the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the legs.
The second way is a simple formula that is unique to squares, and you just need to remember it. As you know, all sides of the square are equal, and that is why mathematicians have calculated the following formula to find its diagonal: it is equal to the product of the side by the root of two.
Of course, it is best to just remember the formula for the length of the diagonal of the square and always use it, because it is much faster and more convenient. This is especially felt when solving problems in the literal form, where instead of whole large root expressions, you can do just one work.
Example
Take, for example, a 6 by 6 square, that is, with a side equal to six centimeters.
In the first way: let the diagonal be equal to C, and the side - A.
Then we get that C = √A ^ 2 + A ^ 2 or C = √2A ^ 2.
We write in numerical form: C = √36 + 36. We got √72, which is 3√8 or 6√2.
And now we find the same diagonal, but by the second method: C = A√2 or in numerical form: 6√2
Now you can see how much the second method is faster, easier and most importantly - more effective, especially in such easy tasks, because every minute is important in the exam!
Other properties of square diagonals
In addition to knowing how to find the diagonals of a square, you also need to know their properties. The main ones are:
- Diagonals are equal to each other and the intersection point is divided in half.
- At the intersection they form right angles.
- Divide the square into equal triangles.
Output
The question of how to count the diagonals of a square is usually asked by students who skipped this topic at school. However, everyone should know such fundamental rules of mathematics! It is advisable to solve as quickly as possible, and this requires knowledge of abbreviated formulas. All this is extremely simple and easy, but at the same time it is the basis necessary for solving much more complex problems in the future. And an important part of this base is square.