The diagonal of a square is 10 cm. What is the length of the side of this square? Give your answer as an exact surd in its simplest form.

Question

The diagonal of a square is 10 cm.
What is the length of the side of this square?
Give your answer as an exact surd in its simplest form.

Answer 1

Let x = the length of a side of the square

a² + b² = c²

x² + x² = 10²

2x² = 100

x² = 50

x = √50

x = 5√2 cm