Final answer:
To find the side of a square given its diagonal, use the diagonal formula for a square. Dividing the diagonal (10 units) by the square root of 2 and rationalizing gives a side length of 5√2 units.
Step-by-step explanation:
To find the length of a side of a square when given the diagonal, you can use the Pythagorean theorem. In this case, the diagonal of the square is 10 units which means the side of the square can be found by dividing the diagonal by the square root of 2.
Using the formula for a diagonal in a square (Diagonal = side × √2), we can set up the following equation:
- Diagonal = side × √2
- 10 = side × √2
- side = 10/√2
- side = 10/√2 × √2/√2 (to rationalize the denominator)
- side = 10√2/2
- side = 5√2 units
The length of each side of the square is 5√2 units.