The rectangle is divided into four parts A, B, C and D. The ratio of Part A to Part B is 6 : 1 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 54 cm2 , find the area of the rectangle.
(a)
A |
B |
C |
D |
6x4 |
1x4 |
|
|
|
4x1 |
1x1 |
|
24 u |
4 u |
1 u |
54 cm2 |
Part B is the repeated identity.
LCM of 1 and 4 = 4
Part A : Part B : Part C = 24 : 4 : 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
24 u + 4 u = 1 u + 54
24 u + 4 u - 1 u = 54
27 u = 54
1 u = 54 ÷ 27 = 2
Area of the rectangle
= 2 x (1 u + 54)
= 2 x (1 x 2 + 54)
= 2 x (2 + 54)
= 2 x 56
= 112 cm
2 Answer(s): (a) 24 : 4 : 1; (b) 112 cm
2