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?
+14917 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 \(3:4\).
!
