The rectangle is divided into four parts Q, R, S and T. The ratio of Part Q to Part R is 10 : 3 and the ratio of Part R to Part S is 3 : 2.
- Find the ratio of Part Q to Part R to Part S.
- Given that Part T is 66 m2 , find the area of the rectangle.
(a)
Q |
R |
S |
T |
10x1 |
3x1 |
|
|
|
3x1 |
2x1 |
|
10 u |
3 u |
2 u |
66 m2 |
Part R is the repeated identity.
LCM of 3 and 3 = 3
Part Q : Part R : Part S = 10 : 3 : 2
(b)
Part Q + Part R = Half of the rectangle
Part S + Part T = Half of the rectangle
Part Q + Part R and Part S + Part T are equal.
Part Q + Part R = Part S + Part T
10 u + 3 u = 2 u + 66
10 u + 3 u - 2 u = 66
11 u = 66
1 u = 66 ÷ 11 = 6
Area of the rectangle
= 2 x (2 u + 66)
= 2 x (2 x 6 + 66)
= 2 x (12 + 66)
= 2 x 78
= 156 m
2 Answer(s): (a) 10 : 3 : 2; (b) 156 m
2