The rectangle is divided into four parts G, H, J and K. The ratio of Part G to Part H is 6 : 5 and the ratio of Part H to Part J is 3 : 2.
- Find the ratio of Part G to Part H to Part J.
- Given that Part K is 23 cm2 , find the area of the rectangle.
(a)
G |
H |
J |
K |
6x3 |
5x3 |
|
|
|
3x5 |
2x5 |
|
18 u |
15 u |
10 u |
23 cm2 |
Part H is the repeated identity.
LCM of 5 and 3 = 15
Part G : Part H : Part J = 18 : 15 : 10
(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
18 u + 15 u = 10 u + 23
18 u + 15 u - 10 u = 23
23 u = 23
1 u = 23 ÷ 23 = 1
Area of the rectangle
= 2 x (10 u + 23)
= 2 x (10 x 1 + 23)
= 2 x (10 + 23)
= 2 x 33
= 66 cm
2 Answer(s): (a) 18 : 15 : 10; (b) 66 cm
2