The rectangle is divided into four parts F, G, H and J. The ratio of Part F to Part G is 9 : 4 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 31 cm2 , find the area of the rectangle.
(a)
F |
G |
H |
J |
9x3 |
4x3 |
|
|
|
3x4 |
2x4 |
|
27 u |
12 u |
8 u |
31 cm2 |
Part G is the repeated identity.
LCM of 4 and 3 = 12
Part F : Part G : Part H = 27 : 12 : 8
(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
27 u + 12 u = 8 u + 31
27 u + 12 u - 8 u = 31
31 u = 31
1 u = 31 ÷ 31 = 1
Area of the rectangle
= 2 x (8 u + 31)
= 2 x (8 x 1 + 31)
= 2 x (8 + 31)
= 2 x 39
= 78 cm
2 Answer(s): (a) 27 : 12 : 8; (b) 78 cm
2