The rectangle is divided into four parts E, F, G and H. The ratio of Part E to Part F is 9 : 1 and the ratio of Part F to Part G is 4 : 1.
- Find the ratio of Part E to Part F to Part G.
- Given that Part H is 39 cm2 , find the area of the rectangle.
(a)
E |
F |
G |
H |
9x4 |
1x4 |
|
|
|
4x1 |
1x1 |
|
36 u |
4 u |
1 u |
39 cm2 |
Part F is the repeated identity.
LCM of 1 and 4 = 4
Part E : Part F : Part G = 36 : 4 : 1
(b)
Part E + Part F = Half of the rectangle
Part G + Part H = Half of the rectangle
Part E + Part F and Part G + Part H are equal.
Part E + Part F = Part G + Part H
36 u + 4 u = 1 u + 39
36 u + 4 u - 1 u = 39
39 u = 39
1 u = 39 ÷ 39 = 1
Area of the rectangle
= 2 x (1 u + 39)
= 2 x (1 x 1 + 39)
= 2 x (1 + 39)
= 2 x 40
= 80 cm
2 Answer(s): (a) 36 : 4 : 1; (b) 80 cm
2