The rectangle is divided into four parts B, C, D and E. The ratio of Part B to Part C is 8 : 3 and the ratio of Part C to Part D is 3 : 2.
- Find the ratio of Part B to Part C to Part D.
- Given that Part E is 45 cm2 , find the area of the rectangle.
(a)
B |
C |
D |
E |
8x1 |
3x1 |
|
|
|
3x1 |
2x1 |
|
8 u |
3 u |
2 u |
45 cm2 |
Part C is the repeated identity.
LCM of 3 and 3 = 3
Part B : Part C : Part D = 8 : 3 : 2
(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
8 u + 3 u = 2 u + 45
8 u + 3 u - 2 u = 45
9 u = 45
1 u = 45 ÷ 9 = 5
Area of the rectangle
= 2 x (2 u + 45)
= 2 x (2 x 5 + 45)
= 2 x (10 + 45)
= 2 x 55
= 110 cm
2 Answer(s): (a) 8 : 3 : 2; (b) 110 cm
2