The rectangle is divided into four parts Z, A, B and C. The ratio of Part Z to Part A is 9 : 1 and the ratio of Part A to Part B is 3 : 1.
- Find the ratio of Part Z to Part A to Part B.
- Given that Part C is 58 cm2 , find the area of the rectangle.
(a)
Z |
A |
B |
C |
9x3 |
1x3 |
|
|
|
3x1 |
1x1 |
|
27 u |
3 u |
1 u |
58 cm2 |
Part A is the repeated identity.
LCM of 1 and 3 = 3
Part Z : Part A : Part B = 27 : 3 : 1
(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
27 u + 3 u = 1 u + 58
27 u + 3 u - 1 u = 58
29 u = 58
1 u = 58 ÷ 29 = 2
Area of the rectangle
= 2 x (1 u + 58)
= 2 x (1 x 2 + 58)
= 2 x (2 + 58)
= 2 x 60
= 120 cm
2 Answer(s): (a) 27 : 3 : 1; (b) 120 cm
2