The length of the diagonal of a square is 8 cm. How long are the sides of the square?

The sides are ##4sqrt2## cm long

Pythagorus tells us that for any right triangle, ##a^2 + b^2 = c^2## where c is the hypotenuse.

A square can be divided into two right triangles along its diagonal, and these triangles are isosceles such that ##a=b##, as all sides of a square are equal.

So we can say that ##a^2+a^2=8^2##, or

##2a^2=64##

##a^2 = 32##

##a=sqrt32=4sqrt2##