The rectangle is divided into four parts Q, R, S and T. The ratio of Part Q to Part R is 6 : 5 and the ratio of Part R to Part S is 3 : 1.
- Find the ratio of Part Q to Part R to Part S.
- Given that Part T is 56 m2 , find the area of the rectangle.
(a)
Q |
R |
S |
T |
6x3 |
5x3 |
|
|
|
3x5 |
1x5 |
|
18 u |
15 u |
5 u |
56 m2 |
Part R is the repeated identity.
LCM of 5 and 3 = 15
Part Q : Part R : Part S = 18 : 15 : 5
(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
18 u + 15 u = 5 u + 56
18 u + 15 u - 5 u = 56
28 u = 56
1 u = 56 ÷ 28 = 2
Area of the rectangle
= 2 x (5 u + 56)
= 2 x (5 x 2 + 56)
= 2 x (10 + 56)
= 2 x 66
= 132 m
2 Answer(s): (a) 18 : 15 : 5; (b) 132 m
2