The rectangle is divided into four parts G, H, J and K. The ratio of Part G to Part H is 9 : 1 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 78 m2 , find the area of the rectangle.
(a)
G |
H |
J |
K |
9x4 |
1x4 |
|
|
|
4x1 |
1x1 |
|
36 u |
4 u |
1 u |
78 m2 |
Part H is the repeated identity.
LCM of 1 and 4 = 4
Part G : Part H : Part J = 36 : 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
36 u + 4 u = 1 u + 78
36 u + 4 u - 1 u = 78
39 u = 78
1 u = 78 ÷ 39 = 2
Area of the rectangle
= 2 x (1 u + 78)
= 2 x (1 x 2 + 78)
= 2 x (2 + 78)
= 2 x 80
= 160 m
2 Answer(s): (a) 36 : 4 : 1; (b) 160 m
2