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# What is the ratio of the area of a square inscribed in a semicircle with radius r

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What is the ratio of the area of a square inscribed in a semicircle with radius r to the area of two congruent squares inscribed in a semicircle with radius r?

Nov 17, 2020

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What is the ratio of the area of a square inscribed in a semicircle with radius r to the area of two congruent squares inscribed in a semicircle with radius r?

Hello Guest!

$$A^2=(r\cdot sin(60°))^2=(r\cdot \frac{\sqrt{3}}{2}))^2=\frac{3}{4}r^2$$

$$2a^2=2\cdot (\frac{r}{\sqrt{2}})^2=r^2$$

$$A^2:2a^2=\frac{3r^2}{4}:r^2=\color{blue}\frac{3}{4}:1=3:4$$

The ratio of the area of a square inscribed in a semicircle with radius r to the area of two congruent squares inscribed in a semicircle $$3:4$$.

!

Nov 17, 2020
edited by asinus  Nov 17, 2020
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The ratio is 0.8   or   4/5

Nov 17, 2020