Calculate the Diagonal of a Rectangle

Q: 3. What is the formula for finding the diagonal of a rectangle?

The formula is d = √(l² + w²), where 'd' is the diagonal, 'l' is the length, and 'w' is the width. This formula is derived from the Pythagorean theorem applied to the right-angled triangle formed by the diagonal, length, and width of the rectangle.

Q: 5. How to find the diagonal of a rectangle step-by-step?

1. Measure the length (l) and width (w) of the rectangle.2. Square both the length and width (l² and w²).3. Add the squared values (l² + w²).4. Find the square root of the sum (√(l² + w²)).5. The result is the length of the diagonal.

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How to Find the Diagonal of a Rectangle Step by Step

Rectangle Diagonal Calculator – Free Online Tool with Formula, Steps & Examples

Rectangle Diagonal Calculator

What is Rectangle Diagonal?

The diagonal of a rectangle is a straight line segment that connects two opposite (non-adjacent) corners of the rectangle. Every rectangle has two diagonals, and both are equal in length. The diagonal cuts across the rectangle, passing through its center, and essentially divides it into two congruent right-angled triangles. The length of the diagonal depends on the rectangle's length and width. Calculating the diagonal is a common step in geometry problems, practical construction measurements, and device screen sizing.

Formula or Logic Behind Rectangle Diagonal Calculator

The formula to calculate the diagonal (d) of a rectangle is derived from the Pythagoras' theorem. The length (l), width (w), and diagonal (d) together form a right triangle, where the diagonal acts as the hypotenuse. The formula is:

d = √(l² + w²)

Here, 'l' stands for the length and 'w' for the width of the rectangle (both must be in the same unit). Just square the length and width, sum them, and take the square root to get the diagonal.

Rectangle Sides and Diagonal Length Table

Length (l)	Width (w)	Diagonal (d)
3 cm	4 cm	5.00 cm
5 cm	12 cm	13.00 cm
8 cm	15 cm	17.00 cm
10 in	24 in	26.00 in
20 ft	21 ft	29.00 ft
16 cm	30 cm	33.94 cm

Steps to Use the Rectangle Diagonal Calculator

Enter the rectangle’s length and width into the input fields.
Select the unit (cm, m, mm, in, or ft) as required.
Click on the 'Calculate' button.
Read your diagonal length instantly displayed below!

Why Use Vedantu’s Rectangle Diagonal Calculator?

Vedantu’s Rectangle Diagonal Calculator is simple, user-friendly, and mobile-responsive. It saves you from manual calculations and instantly gives accurate results for home assignments, construction work, or exam revision. The detailed stepwise solution and explanation help you understand the underlying math concepts. Trusted by students, teachers, and professionals across India, it is updated as per the latest NCERT and board standards.

Real-life Applications of Rectangle Diagonal Calculator

Knowing the diagonal of a rectangle is essential in many day-to-day and academic tasks. For example, manufacturers use it to specify TV or mobile screen sizes, architects measure rooms or tiles, and artists check layouts for posters or packaging. Home DIYers use it to ensure frames or boards are square by verifying diagonals, and engineers use it for bracing and cutting materials. It’s a critical concept in both basic geometry and advanced construction, found in many practical situations.

Explore more helpful tools: Try the HCF Calculator or learn about Prime Numbers.
For more geometry concepts, see Rectangle Properties, or study Pythagorean Triples.

FAQs on Calculate the Diagonal of a Rectangle

1. What is the diagonal of a rectangle?

The diagonal of a rectangle is a line segment connecting two opposite corners (vertices) of the rectangle. It divides the rectangle into two congruent right-angled triangles.

2. How do I calculate the diagonal of a rectangle?

The diagonal (d) of a rectangle can be calculated using the Pythagorean theorem: d = √(l² + w²), where l represents the length and w represents the width of the rectangle.

3. What is the formula for finding the diagonal of a rectangle?

The formula is d = √(l² + w²), where 'd' is the diagonal, 'l' is the length, and 'w' is the width. This formula is derived from the Pythagorean theorem applied to the right-angled triangle formed by the diagonal, length, and width of the rectangle.

4. Are both diagonals of a rectangle equal in length?

Yes, both diagonals of a rectangle are always equal in length. This is a key property of rectangles.

5. How to find the diagonal of a rectangle step-by-step?

1. Measure the length (l) and width (w) of the rectangle.
2. Square both the length and width (l² and w²).
3. Add the squared values (l² + w²).
4. Find the square root of the sum (√(l² + w²)).
5. The result is the length of the diagonal.

6. What are the properties of a rectangle's diagonals?

The diagonals of a rectangle are equal in length, bisect each other (meaning they cut each other in half), and intersect at the center of the rectangle. They also divide the rectangle into two congruent right-angled triangles.

7. Can I use the rectangle diagonal calculator for different units (cm, inches, meters)?

Yes, most rectangle diagonal calculators allow you to input measurements using various units. Ensure you maintain consistency in units for length and width; the output diagonal will be in the same unit.

8. What if I only know the diagonal and width (or length) of the rectangle?

You can still find the unknown side using the Pythagorean theorem. Rearrange the formula: l = √(d² - w²) or w = √(d² - l²), where 'd' is the diagonal, 'l' is the length and 'w' is the width.

9. How is the diagonal of a rectangle related to the Pythagorean theorem?

The diagonal of a rectangle forms the hypotenuse of a right-angled triangle, with the length and width as the other two sides. The Pythagorean theorem (a² + b² = c²) directly applies, where 'a' and 'b' are the length and width, and 'c' is the diagonal.

10. What are some real-world examples where calculating a rectangle's diagonal is useful?

Calculating the diagonal is crucial in various applications. Examples include determining the screen size of a TV or computer monitor, calculating the length of a support brace in construction, or designing layouts in graphic design and other fields.

11. Is the angle formed by the diagonal and sides of a rectangle always 45 degrees?

Only if the rectangle is a square (where length equals width) will the angles formed by the diagonal and sides be 45 degrees. In other rectangles, the angles will vary based on the ratio of length to width.

12. How accurate are online rectangle diagonal calculators?

Most reputable online calculators provide highly accurate results. However, minor discrepancies might arise due to rounding errors in calculations, especially for extremely large or small numbers. Always double-check your inputs for accuracy.