Question

What is the side length of the largest square that can fit into a circle with a radius of 5 units?

Answer 1

Answer:

7.0711 units

Step-by-step explanation:

Given that r=5 units then d=10 units

taking a square of side s, the diagonal has a length of s²+s²≈S×sqrt2

thus S×sqrt 2=10

S=10÷sqrt2

S=50 (Area of the square)

Length of one side of the square= ?

s²=50

s=7.0711units

Answer 2

Answer: 7.07 units.

Step-by-step explanation:

You can draw the figure shown attached, where "d" is the diameter of the circle ($diameter=2*radius=2*5units=10units$).

The measure of the diagonal CB is equal to diameter of the circle and divides the square into two equal right triangles.

Then, you choose any of the triangles and apply the pythagorean theorem to calculate the side lenght of the square:

$CB^{2}=CD^{2}+BD^{2}$

Since it is a square, the sides are equal, then CD=BD. Therefore you can solve for CD as following:

$(CB)^{2}=2(CD)^{2}\\CD=\frac{(CB)^{2}}{2}\\\\CD=\sqrt{\frac{(CB)^{2}}{2}}\\\\CD=\sqrt{\frac{(10units)^{2}}{2}}\\CD=7.07units$