The rectangle is divided into four parts B, C, D and E. The ratio of Part B to Part C is 9 : 2 and the ratio of Part C to Part D is 4 : 1.
- Find the ratio of Part B to Part C to Part D.
- Given that Part E is 21 m2 , find the area of the rectangle.
(a)
B |
C |
D |
E |
9x2 |
2x2 |
|
|
|
4x1 |
1x1 |
|
18 u |
4 u |
1 u |
21 m2 |
Part C is the repeated identity.
LCM of 2 and 4 = 4
Part B : Part C : Part D = 18 : 4 : 1
(b)
Part B + Part C = Half of the rectangle
Part D + Part E = Half of the rectangle
Part B + Part C and Part D + Part E are equal.
Part B + Part C = Part D + Part E
18 u + 4 u = 1 u + 21
18 u + 4 u - 1 u = 21
21 u = 21
1 u = 21 ÷ 21 = 1
Area of the rectangle
= 2 x (1 u + 21)
= 2 x (1 x 1 + 21)
= 2 x (1 + 21)
= 2 x 22
= 44 m
2 Answer(s): (a) 18 : 4 : 1; (b) 44 m
2