The rectangle is divided into four parts E, F, G and H. The ratio of Part E to Part F is 8 : 3 and the ratio of Part F to Part G is 3 : 2.
- Find the ratio of Part E to Part F to Part G.
- Given that Part H is 18 cm2 , find the area of the rectangle.
(a)
E |
F |
G |
H |
8x1 |
3x1 |
|
|
|
3x1 |
2x1 |
|
8 u |
3 u |
2 u |
18 cm2 |
Part F is the repeated identity.
LCM of 3 and 3 = 3
Part E : Part F : Part G = 8 : 3 : 2
(b)
Part E + Part F = Half of the rectangle
Part G + Part H = Half of the rectangle
Part E + Part F and Part G + Part H are equal.
Part E + Part F = Part G + Part H
8 u + 3 u = 2 u + 18
8 u + 3 u - 2 u = 18
9 u = 18
1 u = 18 ÷ 9 = 2
Area of the rectangle
= 2 x (2 u + 18)
= 2 x (2 x 2 + 18)
= 2 x (4 + 18)
= 2 x 22
= 44 cm
2 Answer(s): (a) 8 : 3 : 2; (b) 44 cm
2