Question

PYTHAGORAS MATHS WATCH HELP

Answer 1

Answer:

5.971 cm

Step-by-step explanation:

Use formula $A=\pi r^2$ for the area of the circle. Since the area of the circle is $56\ cm^2,$ then

$\pi r^2=56\\ \\r^2=\dfrac{56}{\pi}\\ \\r=\sqrt{\dfrac{56}{\pi}}$

A square is inscribed into the circle, then its diagonal is twice the radius. The diagonal of the circle is equal to

$d=2r=2\sqrt{\dfrac{56}{\pi}}\ cm$

Let x cm be the length of the square side, then by Pythagorean theorem,

$x^2+x^2=d^2\\ \\2x^2=\left(2\sqrt{\dfrac{56}{\pi}}\right)^2\\ \\2x^2=4\cdot \dfrac{56}{\pi}\\ \\x^2=\dfrac{112}{\pi}\\ \\x=\sqrt{\dfrac{112}{\pi}}\approx 5.971\ cm$