The rectangle is one of the basic geometric shapes. This article will talk about a rectangle and its diagonal, what it is, and how to calculate it. This Diagonal of a Rectangle Calculator helps you calculate the diagonal of a rectangle. Today we are going to learn what exactly is diagonal, how to calculate it, and we are going to solve some problems step-by-step.
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What is the rectangle?
Before answering that question, we should first explain what a rectangle is. The rectangle is a geometric shape with two sides that are mutually the same. The previously mentioned definition is connected to Euclidean space. Euclidean space is most commonly used in classical geometry. Euclid, a Greek mathematician, is responsible for this space. In its early concept, Euclidean space only contained three dimensions. However, we must account that now this space can be any non-negative integer dimension. Therefore, we can better understand the rectangle by looking at the example below.
In the previous figure, we can notice that rectangle has four sides where two opposite sides have the same length. Not only that, but all the angles in the rectangle are 90 degrees. The sum of angles in a rectangle is equal to 360 degrees. In the previous figure, x represents length, while y represents the width. Sometimes you might come across different notations of the length of the rectangle and width of the rectangle. Most notable “w” is used for marking the width of the rectangle, while italic “l” is used for length.
What is the diagonal of the rectangle?
Now we can discuss the diagonal line of the rectangle. The diagonal line is a straight line that connects the two farthest points in the rectangle. In short, this line divides the angle of one corner of the rectangle. It divides it into two parts or two new angles.
Another thing that we can conclude would be the new shape we have after we draw a diagonal line. These shapes are triangles, and their hypotenuse is diagonal to the rectangle. The hypotenuse is the longest side in right-angle triangles. Right angle triangles are triangles that have one angle that is 90 degrees. Notice how it has to be 90 degrees. If we do not have that 90-degree angle, the triangle is known as a non-right triangle.
We have a simple example of the rectangle and its diagonal line in the next figure.
To sum up, rectangles are two triangles. One of these triangles is upside down concerning the other. Therefore, we can apply the hypotenuse of these two triangles to calculate the diagonal. The diagonal line is a line that connects two opposite corners. Therefore, these triangles are the same.
How to find the diagonal length of a rectangle?
For easier understanding, we are going to use the previous figure. From that figure, we can notice two triangles. We are going to focus on the upper triangle for now. To calculate the diagonal line, we will use the Pythagoras theorem. Pythagoras theorem states that hypotenuse squared equals the square of the two remaining sides in the right-angle triangle. We can write the Pythagoras theorem as:
Pythagoras lived from 570 years B.C to 490 B.C. Pythagoras was truly the real mathematician. However, he mostly worked on geometry and trigonometry-the most useful branches of mathematics in ancient times.
What’s the diagonal of a rectangle formula?
We employ the Pythagoras formula to calculate the diagonal. We mark two sides with italic. For example, we can use the shorter side as “a” while the longer side is marked as “b.” We can also mark the length of the diagonal line as “d.” If we insert these values into the Pythagorean theorem, we get:
Some textbooks also use different notations for the length of the diagonal line. For example, l as in length of the diagonal line.
Problem 1: Calculate the diagonal line of the rectangle if the larger side of the rectangle is 10 cm, the shorter side is 7 cm. We are given two sides of the rectangle. It is important to note that we are going to use metric units instead of imperial units to calculate the length of the diagonal line for this problem.
Using Pythagoras formula, we get:
Notice that the diagonal line is longer than side a and side b but shorter than the sum of two sides. Therefore, there cannot be a rectangle whose sum of sides is less than the diagonal.
Diagonal of a Rectangle Calculator – How to use?
To use our diagonal of a rectangle calculator, download our calcon mobile app from the google play store or the apple store. Then, to calculate the diagonal, you need to follow these simple steps:
- Enter longer side
- Enter shorter side
- Read your results such as Area, Perimeter, Angle between diagonals, Circumcircle radius and finally the length of a diagonal.
With our calculator, you can obtain all the rectangle parameter values by entering just the length of the sides.
How to find the diagonal length of a rectangle?
We utilize the diagonal rectangle formula to find the diagonal length. The mentioned formula is just the Pythagoras theorem from created triangle when connecting two farthest points.
Are diagonals of a rectangle perpendicular?
No, they are not. Only for square and rhombus, the diagonals are perpendicular to each other, but for rectangles, parallelograms, the diagonals are not perpendicular.
Are the diagonals of a rectangle equal?
Yes. Both diagonals are equal. We can prove this by calculating the hypotenuse of both triangles created from the rectangle.
What if we do not know one side of the rectangle?
If we do not know one side of the rectangle, we can use one of the trigonometric functions to calculate the hypotenuse. For example, if we do not know the upper side “b,” then we may utilize cosine to calculate the hypotenuse, or in this case, diagonal of the rectangle.
Are diagonals splitting the corners of the rectangle equally?
No. Only diagonals of rhomboids are splitting 90-degree angles equally into two 45 degrees angles.