The rectangle is divided into four parts Z, A, B and C. The ratio of Part Z to Part A is 7 : 2 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 75 cm2 , find the area of the rectangle.
(a)
Z |
A |
B |
C |
7x3 |
2x3 |
|
|
|
3x2 |
1x2 |
|
21 u |
6 u |
2 u |
75 cm2 |
Part A is the repeated identity.
LCM of 2 and 3 = 6
Part Z : Part A : Part B = 21 : 6 : 2
(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
21 u + 6 u = 2 u + 75
21 u + 6 u - 2 u = 75
25 u = 75
1 u = 75 ÷ 25 = 3
Area of the rectangle
= 2 x (2 u + 75)
= 2 x (2 x 3 + 75)
= 2 x (6 + 75)
= 2 x 81
= 162 cm
2 Answer(s): (a) 21 : 6 : 2; (b) 162 cm
2