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 4 : 1.
- Find the ratio of Part F to Part G to Part H.
- Given that Part J is 84 cm2 , find the area of the rectangle.
(a)
F |
G |
H |
J |
9x1 |
4x1 |
|
|
|
4x1 |
1x1 |
|
9 u |
4 u |
1 u |
84 cm2 |
Part G is the repeated identity.
LCM of 4 and 4 = 4
Part F : Part G : Part H = 9 : 4 : 1
(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
9 u + 4 u = 1 u + 84
9 u + 4 u - 1 u = 84
12 u = 84
1 u = 84 ÷ 12 = 7
Area of the rectangle
= 2 x (1 u + 84)
= 2 x (1 x 7 + 84)
= 2 x (7 + 84)
= 2 x 91
= 182 cm
2 Answer(s): (a) 9 : 4 : 1; (b) 182 cm
2