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 3 : 2.
- Find the ratio of Part A to Part B to Part C.
- Given that Part D is 40 cm2 , find the area of the rectangle.
(a)
A |
B |
C |
D |
7x1 |
3x1 |
|
|
|
3x1 |
2x1 |
|
7 u |
3 u |
2 u |
40 cm2 |
Part B is the repeated identity.
LCM of 3 and 3 = 3
Part A : Part B : Part C = 7 : 3 : 2
(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
7 u + 3 u = 2 u + 40
7 u + 3 u - 2 u = 40
8 u = 40
1 u = 40 ÷ 8 = 5
Area of the rectangle
= 2 x (2 u + 40)
= 2 x (2 x 5 + 40)
= 2 x (10 + 40)
= 2 x 50
= 100 cm
2 Answer(s): (a) 7 : 3 : 2; (b) 100 cm
2