The rectangle is divided into four parts F, G, H and J. The ratio of Part F to Part G is 8 : 3 and the ratio of Part G to Part H is 3 : 2.
- Find the ratio of Part F to Part G to Part H.
- Given that Part J is 81 cm2 , find the area of the rectangle.
(a)
F |
G |
H |
J |
8x1 |
3x1 |
|
|
|
3x1 |
2x1 |
|
8 u |
3 u |
2 u |
81 cm2 |
Part G is the repeated identity.
LCM of 3 and 3 = 3
Part F : Part G : Part H = 8 : 3 : 2
(b)
Part F + Part G = Half of the rectangle
Part H + Part J = Half of the rectangle
Part F + Part G and Part H + Part J are equal.
Part F + Part G = Part H + Part J
8 u + 3 u = 2 u + 81
8 u + 3 u - 2 u = 81
9 u = 81
1 u = 81 ÷ 9 = 9
Area of the rectangle
= 2 x (2 u + 81)
= 2 x (2 x 9 + 81)
= 2 x (18 + 81)
= 2 x 99
= 198 cm
2 Answer(s): (a) 8 : 3 : 2; (b) 198 cm
2