The length of the diagonal of a rectangle can be calculated using the Pythagorean theorem: it is the square root of the sum of the squares of the length and width.
To find the length of the diagonal, you can use the following formula:
d = √(l² + w²)
Where:
- d = length of the diagonal
- l = length of the rectangle
- w = width of the rectangle
Explanation:
The diagonal of a rectangle divides it into two right-angled triangles. The diagonal acts as the hypotenuse of these triangles, while the length and width of the rectangle serve as the other two sides (legs) of the triangle. According to the Pythagorean theorem (a² + b² = c²), where 'c' is the hypotenuse, the square of the diagonal is equal to the sum of the squares of the length and width. Therefore, by taking the square root of the sum of the squares of the length and width, you can find the length of the diagonal.
Example:
Suppose a rectangle has a length of 4 units and a width of 3 units.
- Square the length: 4² = 16
- Square the width: 3² = 9
- Add the squares: 16 + 9 = 25
- Take the square root: √25 = 5
Therefore, the length of the diagonal of the rectangle is 5 units.
