If you’ve ever encountered a rhombus, you probably know that it’s a quadrilateral with all sides equal in length. However, what if you’re given the lengths of the diagonals of a rhombus and need to find the length of its sides? In this guide, we’ll walk you through the steps to calculate the side length of a rhombus with given diagonals.

Understanding the Diagonals of a Rhombus

Before diving into the calculation, let’s make sure we understand the diagonals of a rhombus. A rhombus has two diagonals – each connecting opposite vertices. These diagonals bisect each other at a 90-degree angle, dividing the rhombus into four congruent right triangles.

The Formula for Calculating the Rhombus’s Side Length

To find the length of a rhombus’s side, given the lengths of its diagonals, you can use the formula:

  • Side Length (s) = √[(Diagonal 1/2)^2 + (Diagonal 2/2)^2]

Step-by-Step Calculation

Let’s break down the calculation into simple steps:

  1. Step 1: Start by halving the lengths of the given diagonals.
  2. Step 2: Square each halved diagonal length.
  3. Step 3: Add the squared values from Step 2 together.
  4. Step 4: Take the square root of the sum obtained in Step 3.
  5. Step 5: The result from Step 4 is the length of each side of the rhombus.

An Example Calculation

Let’s say we have a rhombus with diagonals measuring 8cm and 6cm. Applying the steps mentioned above, we find:

  1. Step 1: Halving the diagonals gives us 4cm and 3cm.
  2. Step 2: Squaring each halved diagonal, we get 16cm² and 9cm².
  3. Step 3: Adding the squared values together, we obtain 25cm².
  4. Step 4: Taking the square root of 25cm² results in 5cm.
  5. Step 5: Therefore, each side of the rhombus measures 5cm.

Finding the length of a rhombus’s side with given diagonals is a straightforward calculation that involves halving the diagonals, squaring each half, summing the squared values, and finally taking the square root. By following the step-by-step guide and using the provided formula, you can easily determine the side length of any rhombus given its diagonals.

Happy rhombus calculations!

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