The rectangle is divided into four parts A, B, C and D. The ratio of Part A to Part B is 7 : 3 and the ratio of Part B to Part C is 4 : 1.
- Find the ratio of Part A to Part B to Part C.
- Given that Part D is 74 m2 , find the area of the rectangle.
(a)
A |
B |
C |
D |
7x4 |
3x4 |
|
|
|
4x3 |
1x3 |
|
28 u |
12 u |
3 u |
74 m2 |
Part B is the repeated identity.
LCM of 3 and 4 = 12
Part A : Part B : Part C = 28 : 12 : 3
(b)
Part A + Part B = Half of the rectangle
Part C + Part D = Half of the rectangle
Part A + Part B and Part C + Part D are equal.
Part A + Part B = Part C + Part D
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