The rectangle is divided into four parts F, G, H and J. The ratio of Part F to Part G is 10 : 1 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 86 m2 , find the area of the rectangle.
(a)
F |
G |
H |
J |
10x4 |
1x4 |
|
|
|
4x1 |
1x1 |
|
40 u |
4 u |
1 u |
86 m2 |
Part G is the repeated identity.
LCM of 1 and 4 = 4
Part F : Part G : Part H = 40 : 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
40 u + 4 u = 1 u + 86
40 u + 4 u - 1 u = 86
43 u = 86
1 u = 86 ÷ 43 = 2
Area of the rectangle
= 2 x (1 u + 86)
= 2 x (1 x 2 + 86)
= 2 x (2 + 86)
= 2 x 88
= 176 m
2 Answer(s): (a) 40 : 4 : 1; (b) 176 m
2