The rectangle is divided into four parts G, H, J and K. The ratio of Part G to Part H is 9 : 4 and the ratio of Part H to Part J is 4 : 1.
- Find the ratio of Part G to Part H to Part J.
- Given that Part K is 96 cm2 , find the area of the rectangle.
(a)
G |
H |
J |
K |
9x1 |
4x1 |
|
|
|
4x1 |
1x1 |
|
9 u |
4 u |
1 u |
96 cm2 |
Part H is the repeated identity.
LCM of 4 and 4 = 4
Part G : Part H : Part J = 9 : 4 : 1
(b)
Part G + Part H = Half of the rectangle
Part J + Part K = Half of the rectangle
Part G + Part H and Part J + Part K are equal.
Part G + Part H = Part J + Part K
9 u + 4 u = 1 u + 96
9 u + 4 u - 1 u = 96
12 u = 96
1 u = 96 ÷ 12 = 8
Area of the rectangle
= 2 x (1 u + 96)
= 2 x (1 x 8 + 96)
= 2 x (8 + 96)
= 2 x 104
= 208 cm
2 Answer(s): (a) 9 : 4 : 1; (b) 208 cm
2