The rectangle is divided into four parts Q, R, S and T. The ratio of Part Q to Part R is 9 : 5 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 96 cm2 , find the area of the rectangle.
(a)
Q |
R |
S |
T |
9x3 |
5x3 |
|
|
|
3x5 |
2x5 |
|
27 u |
15 u |
10 u |
96 cm2 |
Part R is the repeated identity.
LCM of 5 and 3 = 15
Part Q : Part R : Part S = 27 : 15 : 10
(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
27 u + 15 u = 10 u + 96
27 u + 15 u - 10 u = 96
32 u = 96
1 u = 96 ÷ 32 = 3
Area of the rectangle
= 2 x (10 u + 96)
= 2 x (10 x 3 + 96)
= 2 x (30 + 96)
= 2 x 126
= 252 cm
2 Answer(s): (a) 27 : 15 : 10; (b) 252 cm
2