You can find the diagonal of a square using the Pythagorean theorem.
Understanding the Relationship
- A square has four equal sides and four right angles.
- The diagonal of a square divides it into two right-angled triangles.
- The diagonal of the square acts as the hypotenuse of these triangles.
Applying the Pythagorean Theorem
The Pythagorean theorem states: a² + b² = c², where:
- a and b are the lengths of the two shorter sides of a right-angled triangle.
- c is the length of the hypotenuse.
In the case of a square, the two shorter sides of the right-angled triangle formed by the diagonal are the sides of the square (both equal to a). Therefore:
- a² + a² = c²
- 2a² = c²
- c = √(2a²) = a√2
Therefore, the diagonal of a square with side a is a√2.
Example
Let's say the side of a square is 5 cm. To find the diagonal:
- a = 5 cm
- c = a√2 = 5√2 cm
The diagonal of the square is 5√2 cm.
