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 4 : 1.
- Find the ratio of Part B to Part C to Part D.
- Given that Part E is 41 cm2 , find the area of the rectangle.
(a)
B |
C |
D |
E |
8x4 |
3x4 |
|
|
|
4x3 |
1x3 |
|
32 u |
12 u |
3 u |
41 cm2 |
Part C is the repeated identity.
LCM of 3 and 4 = 12
Part B : Part C : Part D = 32 : 12 : 3
(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
32 u + 12 u = 3 u + 41
32 u + 12 u - 3 u = 41
41 u = 41
1 u = 41 ÷ 41 = 1
Area of the rectangle
= 2 x (3 u + 41)
= 2 x (3 x 1 + 41)
= 2 x (3 + 41)
= 2 x 44
= 88 cm
2 Answer(s): (a) 32 : 12 : 3; (b) 88 cm
2