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astra-53 [7]
3 years ago
5

PYTHAGORAS MATHS WATCH HELP

Mathematics
1 answer:
Airida [17]3 years ago
6 0

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

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