What is equal to the diagonal of the square

Square is the simplest figure in geometry. It is from her, a rectangle and square begin to study this subject. The ability to solve the task with a square will help you to master a more complex material. This article will tell you how to find the diagonal of the square.

The solution of geometric tasks is interesting to solve them in several ways. Every way is interesting in its own way. No exception and diagonal of the square, which can be found direct and indirect paths.

1

How to find a square diagonal - formula

There is a pretty simple formula for finding a diagonal of a square. It looks like this: a√2. A - Square side. Recall that all sides of the square are equal. Thus, if you know the size of the one hand, you know the size of the other three sides. To find out the diagonal of the square, it is necessary to multiply its side to the root of two.

Example 1: Find the diagonal of the square, if it is known that his side is 5.

Solution: Substituting the value in the aforementioned formula, it is not difficult to guess that the diagonal will be equal to 5√2.

Example 2: Find the side of the square, if it is known that its diagonal is 5√2.

Solution: Diagonal is denoted by a small Latin letter d. D \u003d A√2. Therefore, to find the side of knowing diagonal, it is necessary to divide the diagonal to the root of two. Having done this action, we learn the side of the square, which, in this case, is 5.

2

How to find a square diagonal through a rectangular triangle

If you have a diagonal in the square, it is easy to notice that two rectangular triangles are formed. Recall that a rectangular triangle has one angle necessarily straight. It consists of two cathets (the side at an angle of 90 degrees) and hypotenuses (the opposite of the 90-degrads corner of the side). The square of the hypotenuse is equal to the sum of the squares of the cathets. In this case, hypotenuse is the diagonal of our square. Since kartets are the sides of the square, the formula will have the following form: D² \u003d A² + a² \u003d 2a². It follows that d \u003d √2a² \u003d a√2.

Example 3: Find the diagonal of the square if his side is 3.

Solution:

1. We fold the squares of the parties, we get 18.
2. We consider the root of 18 and get 3√2.

Despite the fact that the last method is longer and ultimately we go out on the formula from the first example, it is necessary to know it. In essence, this method is proof of the formula of the square diagonal. It is this proof that can come to the exam or the Olympiad. Good learn her, because she can help you at the aforementioned events.

3

Online calculator

Despite the fact that it is not difficult to solve such tasks, some students can forget the formula. For such cases, there is an online calculator that allows you to find the correct answer based on what is given in the task. To use this service, go to link.

1. Scroll down the page down and you will find the subtitle "Find a diagonal of a square, knowing the side.
2. Below this subtitle will be given the formula, looking at which you do not need a calculator.
3. But still, if you are not sure, enter the value of the length of the square in the field, and then on the "Calculate" button.
4. Calculator for 1 second will give you the correct answer.

Now, knowing several ways to solve the task of this topic, you will not flip the book on mathematics in search of the desired formula, but simply use the online calculator or examples that are given above.