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# How to calculate the length of a diagonal in a rectangle (oblong).

To work out the length of a diagonal of a rectangle first you need to divide the rectangle into two right angled triangles. All you need to do now is apply Pythagoras to one of the right angled triangles, as the length of the diagonal of the rectangle is the same as working out the length of the hypotenuse in the right angled triangle. To do this either use a² + b² = c², or if you don’t like algebra, square the two side lengths, add them together and square root your final answer.

**Example 1**

A rectangle has a length of 8cm and a width of 3cm. Work out the length of the diagonal.

First split your triangle into two right angled triangles and apply Pythagoras Theorem.

Square the 2 sides:

8² = 64

3² = 9

Add these together:

64 + 9 = 73

√73 = 8.5 cm to 1 decimal place.

Or use a² + b² = c² where c is the length of the hypotenuse (the longest side of the right angled triangle).

8² + 3² = c²

64 + 9 = c²

73 = c² (square root)

8.5 = c

So the diagonal of the rectangle has a length of 8.5cm.

**Example 2**

A rectangle has a length of 11cm and a width of 5cm. Work out the length of the diagonal.

Just like example 1, split your triangle into two right angled triangles and again use Pythagoras. Square the 2 sides:

11² = 121

5² = 25

Add these together:

121 + 25 = 146

√146 = 12.1 cm to 1 decimal place.

Or use a² + b² = c² where c is the length of the hypotenuse (the longest side of the right angled triangle).

11² + 5² = c²

121 + 25 = c²

146 = c² (square root)

12.1 = c

So the length of the diagonal of the rectangle is 12.1cm

So basically, all you need to do to work out the length of the diagonal of a rectangle is to; square the length and width of the rectangle, add these numbers together and square root your answer.

## Comments

You've done it again catman3000! The simplistic, yet highly effective approach, makes learning these formulae very easy. I am still wondering if you could include work areas where this formula is implemented. Thanks.

The is simply amazing and easy to understand. I used that kind of technique with my students in 3rd year high school. Students nowadays hate mathematics especially if they cannot understand the problem, however, given them some lessons with practical applications to life, their interest to solve mathematical problems will improve. Giving them formula to memorize is nonsense without understanding how it works. In geometry subjects, you need illustrations to help students solve the problems.. Good job catman300 ( http://www.farmvillefcu.com/)