2019 · Q55
What is the ratio of the area of a square inscribed in a semicircle of radius r to the area of a square inscribed in a circle of radius r?
Elementary MathematicsMensuration
- A1:2
- B2:5
- C2:3
- D3:5
Explanation
Square in circle radius r: diagonal 2r, area 2r^2. Square in semicircle: with side s on the diameter, (s/2)^2+s^2 = r^2 gives s^2 = 4r^2/5. Ratio = (4r^2/5)/(2r^2) = 2:5.