The rectangle is divided into four parts R, S, T and U. The ratio of Part R to Part S is 9 : 2 and the ratio of Part S to Part T is 3 : 1.
- Find the ratio of Part R to Part S to Part T.
- Given that Part U is 31 m2 , find the area of the rectangle.
(a)
R |
S |
T |
U |
9x3 |
2x3 |
|
|
|
3x2 |
1x2 |
|
27 u |
6 u |
2 u |
31 m2 |
Part S is the repeated identity.
LCM of 2 and 3 = 6
Part R : Part S : Part T = 27 : 6 : 2
(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
27 u + 6 u = 2 u + 31
27 u + 6 u - 2 u = 31
31 u = 31
1 u = 31 ÷ 31 = 1
Area of the rectangle
= 2 x (2 u + 31)
= 2 x (2 x 1 + 31)
= 2 x (2 + 31)
= 2 x 33
= 66 m
2 Answer(s): (a) 27 : 6 : 2; (b) 66 m
2