The rectangle is divided into four parts A, B, C and D. The ratio of Part A to Part B is 10 : 3 and the ratio of Part B to Part C is 3 : 1.
- Find the ratio of Part A to Part B to Part C.
- Given that Part D is 72 cm2 , find the area of the rectangle.
(a)
A |
B |
C |
D |
10x1 |
3x1 |
|
|
|
3x1 |
1x1 |
|
10 u |
3 u |
1 u |
72 cm2 |
Part B is the repeated identity.
LCM of 3 and 3 = 3
Part A : Part B : Part C = 10 : 3 : 1
(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
10 u + 3 u = 1 u + 72
10 u + 3 u - 1 u = 72
12 u = 72
1 u = 72 ÷ 12 = 6
Area of the rectangle
= 2 x (1 u + 72)
= 2 x (1 x 6 + 72)
= 2 x (6 + 72)
= 2 x 78
= 156 cm
2 Answer(s): (a) 10 : 3 : 1; (b) 156 cm
2