The rectangle is divided into four parts R, S, T and U. The ratio of Part R to Part S is 6 : 5 and the ratio of Part S to Part T is 3 : 2.
- Find the ratio of Part R to Part S to Part T.
- Given that Part U is 69 m2 , find the area of the rectangle.
(a)
R |
S |
T |
U |
6x3 |
5x3 |
|
|
|
3x5 |
2x5 |
|
18 u |
15 u |
10 u |
69 m2 |
Part S is the repeated identity.
LCM of 5 and 3 = 15
Part R : Part S : Part T = 18 : 15 : 10
(b)
Part R + Part S = Half of the rectangle
Part T + Part U = Half of the rectangle
Part R + Part S and Part T + Part U are equal.
Part R + Part S = Part T + Part U
18 u + 15 u = 10 u + 69
18 u + 15 u - 10 u = 69
23 u = 69
1 u = 69 ÷ 23 = 3
Area of the rectangle
= 2 x (10 u + 69)
= 2 x (10 x 3 + 69)
= 2 x (30 + 69)
= 2 x 99
= 198 m
2 Answer(s): (a) 18 : 15 : 10; (b) 198 m
2