The rectangle is divided into four parts F, G, H and J. The ratio of Part F to Part G is 6 : 5 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 78 cm2 , find the area of the rectangle.
(a)
F |
G |
H |
J |
6x4 |
5x4 |
|
|
|
4x5 |
1x5 |
|
24 u |
20 u |
5 u |
78 cm2 |
Part G is the repeated identity.
LCM of 5 and 4 = 20
Part F : Part G : Part H = 24 : 20 : 5
(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
24 u + 20 u = 5 u + 78
24 u + 20 u - 5 u = 78
39 u = 78
1 u = 78 ÷ 39 = 2
Area of the rectangle
= 2 x (5 u + 78)
= 2 x (5 x 2 + 78)
= 2 x (10 + 78)
= 2 x 88
= 176 cm
2 Answer(s): (a) 24 : 20 : 5; (b) 176 cm
2