PSLE The figure shows a rectangle with its corners cut out. Each of the 4 identical corners cut out is a quarter circle. The ratio of the length of the rectangle to its breadth is 5 : 3.
- What is the radius of each quarter circle?
- What is the perimeter of the shaded part. Take π = 3.14. Give your answer correct to 1 decimal place.
Length of the rectangle
= 5 u
= 2 radii + 17
Breadth of the rectangle
= 3 u
= 2 radii + 3
5 u - 3 u = (2 radii) + 17 - (2 radii + 3)
2 u = 17 - 3
2 u = 14
1 u = 14 ÷ 2 = 7
3 u = 3 x 7 = 21
Radius of the quarter circle
= (21 - 3) ÷ 2
= 18 ÷ 2
= 9 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 18
= 56.52 cm
Perimeter of the shaded part
= 56.52 + 17 + 17 + 3 + 3
= 96.52 cm
≈ 96.5 cm (Correct to 1 decimal place)
Answer(s): (a) 9 cm; (b) 96.5 cm