Answer
the length of the side of the square is $2.83in$
Work Step by Step
We can see that the diameter of the circle divides the square into 2 isosceles right triangles.
We use the Pythagorean Theorem to solve this exercise.
$c^{2}=a^{2}+b^{2}$
Given data:
$hypotenuse=diameter=c=4.00in$
Because it is an isosceles triangle, we know that: $a=b$
Simplify the formula:
$c^{2}=a^{2}+a^{2}$
$c^{2}=2a^{2}$
$a^{2}=\frac{c^{2}}{2}$
$a=\sqrt \frac{c^{2}}{2}$
So,
$a=\sqrt \frac{(4in)^{2}}{2}=2.83in$
