The rectangle is divided into four parts R, S, T and U. The ratio of Part R to Part S is 6 : 1 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 95 cm2 , find the area of the rectangle.
(a)
R |
S |
T |
U |
6x3 |
1x3 |
|
|
|
3x1 |
2x1 |
|
18 u |
3 u |
2 u |
95 cm2 |
Part S is the repeated identity.
LCM of 1 and 3 = 3
Part R : Part S : Part T = 18 : 3 : 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
18 u + 3 u = 2 u + 95
18 u + 3 u - 2 u = 95
19 u = 95
1 u = 95 ÷ 19 = 5
Area of the rectangle
= 2 x (2 u + 95)
= 2 x (2 x 5 + 95)
= 2 x (10 + 95)
= 2 x 105
= 210 cm
2 Answer(s): (a) 18 : 3 : 2; (b) 210 cm
2