The rectangle is divided into four parts A, B, C and D. The ratio of Part A to Part B is 6 : 5 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 84 m2 , find the area of the rectangle.
(a)
A |
B |
C |
D |
6x3 |
5x3 |
|
|
|
3x5 |
1x5 |
|
18 u |
15 u |
5 u |
84 m2 |
Part B is the repeated identity.
LCM of 5 and 3 = 15
Part A : Part B : Part C = 18 : 15 : 5
(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
18 u + 15 u = 5 u + 84
18 u + 15 u - 5 u = 84
28 u = 84
1 u = 84 ÷ 28 = 3
Area of the rectangle
= 2 x (5 u + 84)
= 2 x (5 x 3 + 84)
= 2 x (15 + 84)
= 2 x 99
= 198 m
2 Answer(s): (a) 18 : 15 : 5; (b) 198 m
2