The rectangle is divided into four parts Z, A, B and C. The ratio of Part Z to Part A is 8 : 5 and the ratio of Part A to Part B is 4 : 1.
- Find the ratio of Part Z to Part A to Part B.
- Given that Part C is 47 cm2 , find the area of the rectangle.
(a)
Z |
A |
B |
C |
8x4 |
5x4 |
|
|
|
4x5 |
1x5 |
|
32 u |
20 u |
5 u |
47 cm2 |
Part A is the repeated identity.
LCM of 5 and 4 = 20
Part Z : Part A : Part B = 32 : 20 : 5
(b)
Part Z + Part A = Half of the rectangle
Part B + Part C = Half of the rectangle
Part Z + Part A and Part B + Part C are equal.
Part Z + Part A = Part B + Part C
32 u + 20 u = 5 u + 47
32 u + 20 u - 5 u = 47
47 u = 47
1 u = 47 ÷ 47 = 1
Area of the rectangle
= 2 x (5 u + 47)
= 2 x (5 x 1 + 47)
= 2 x (5 + 47)
= 2 x 52
= 104 cm
2 Answer(s): (a) 32 : 20 : 5; (b) 104 cm
2