When it comes to geometry, rectangles are among the most commonly known and understood shapes. One important aspect of a rectangle that is often overlooked is calculating its diagonal. A diagonal is a straight line that connects two opposite corners in a rectangle. Calculating the diagonal length accurately is essential in various professions and daily tasks, such as engineering, architecture, or simply measuring the size of electronic devices like televisions or computer monitors.

In this article, we’ll be discussing how to calculate the diagonal of a rectangle using the Pythagorean theorem. Don’t worry if you’re not familiar with this mathematical principle – we’ve got you covered!

Understanding Rectangles & Diagonals

A rectangle is a parallelogram consisting of four right angles. It has two pairs of equal, parallel sides – one pair being the longer sides called ‘length,’ and the other pair being the shorter sides called ‘width.’ The line connecting any two non-adjacent vertices (opposite corners) in the rectangle is known as its diagonal.

Calculating Diagonal using Pythagorean Theorem

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposing the right angle) is equal to the sum of squares of lengths of other two sides. In simpler terms: `a² + b² = c²`, where “a” and “b” represent the triangle’s legs and “c” represents its hypotenuse.

For calculating a rectangle’s diagonal, we can use this theorem because splitting a rectangle along its diagonal forms two right-angled triangles with equal dimensions. Here’s how it can be applied:

1. Note down your rectangle’s dimensions: length (l) and width (w).

2. Use the Pythagorean theorem formula to calculate its diagonal:

Diagonal² = Length² + Width²

Diagonal² = l² + w²

3. Calculate the diagonal (d) by finding the square root of the sum obtained in step 2:

Diagonal (d) = √(l² + w²)

Example:

Let’s say we have a rectangle with a length of 12 units and a width of 5 units. To find its diagonal, we’ll follow the steps mentioned above:

1. Length (l) = 12 units

Width (w) = 5 units

2. Diagonal² = l² + w²

Diagonal² = 12² + 5²

Diagonal² = 144 + 25

Diagonal² = 169

3. Diagonal (d) = √169

Diagonal (d) = 13 units

So, the diagonal of the rectangle is 13 units long.

This method of calculating a rectangle’s diagonal proves helpful for various purposes, from designing furniture to estimating dimensions for home décor. With this knowledge, you can now effortlessly and accurately calculate the diagonal of any given rectangle.