The rectangle is divided into four parts A, B, C and D. The ratio of Part A to Part B is 9 : 2 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 58 m2 , find the area of the rectangle.
(a)
A |
B |
C |
D |
9x3 |
2x3 |
|
|
|
3x2 |
2x2 |
|
27 u |
6 u |
4 u |
58 m2 |
Part B is the repeated identity.
LCM of 2 and 3 = 6
Part A : Part B : Part C = 27 : 6 : 4
(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
27 u + 6 u = 4 u + 58
27 u + 6 u - 4 u = 58
29 u = 58
1 u = 58 ÷ 29 = 2
Area of the rectangle
= 2 x (4 u + 58)
= 2 x (4 x 2 + 58)
= 2 x (8 + 58)
= 2 x 66
= 132 m
2 Answer(s): (a) 27 : 6 : 4; (b) 132 m
2