The rectangle is divided into four parts Z, A, B and C. The ratio of Part Z to Part A is 7 : 3 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 74 m2 , find the area of the rectangle.
(a)
Z |
A |
B |
C |
7x4 |
3x4 |
|
|
|
4x3 |
1x3 |
|
28 u |
12 u |
3 u |
74 m2 |
Part A is the repeated identity.
LCM of 3 and 4 = 12
Part Z : Part A : Part B = 28 : 12 : 3
(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
28 u + 12 u = 3 u + 74
28 u + 12 u - 3 u = 74
37 u = 74
1 u = 74 ÷ 37 = 2
Area of the rectangle
= 2 x (3 u + 74)
= 2 x (3 x 2 + 74)
= 2 x (6 + 74)
= 2 x 80
= 160 m
2 Answer(s): (a) 28 : 12 : 3; (b) 160 m
2