The rectangle is divided into four parts Q, R, S and T. The ratio of Part Q to Part R is 9 : 1 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 87 m2 , find the area of the rectangle.
(a)
Q |
R |
S |
T |
9x3 |
1x3 |
|
|
|
3x1 |
1x1 |
|
27 u |
3 u |
1 u |
87 m2 |
Part R is the repeated identity.
LCM of 1 and 3 = 3
Part Q : Part R : Part S = 27 : 3 : 1
(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 + 3 u = 1 u + 87
27 u + 3 u - 1 u = 87
29 u = 87
1 u = 87 ÷ 29 = 3
Area of the rectangle
= 2 x (1 u + 87)
= 2 x (1 x 3 + 87)
= 2 x (3 + 87)
= 2 x 90
= 180 m
2 Answer(s): (a) 27 : 3 : 1; (b) 180 m
2