The diagonal of a square is 2 cm. What is the length of the side of this square?
Give your answer as an exact surd in its simplest form

Step-by-step explanation:

The diagonal splits the square into 2 right triangles, with hypotenuse the diagonal of length 2 and congruent sides x

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides , then

x² + x² = 2²

2x² = 4 ( divide both sides by 2 )

x² = 2 ( take square root of both sides )

x = ← length of side of the square

step-by-step explanation :

we know that

the measurement of the outer angle is the semi-difference of the arcs which comprises

in this problem

m< xzy is the outer angle

substitute the values

the measure of angle xoy is equal to

> by central angle

substitute the value