The rectangle is divided into four parts R, S, T and U. The ratio of Part R to Part S is 7 : 1 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 92 cm2 , find the area of the rectangle.
(a)
R |
S |
T |
U |
7x3 |
1x3 |
|
|
|
3x1 |
1x1 |
|
21 u |
3 u |
1 u |
92 cm2 |
Part S is the repeated identity.
LCM of 1 and 3 = 3
Part R : Part S : Part T = 21 : 3 : 1
(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
21 u + 3 u = 1 u + 92
21 u + 3 u - 1 u = 92
23 u = 92
1 u = 92 ÷ 23 = 4
Area of the rectangle
= 2 x (1 u + 92)
= 2 x (1 x 4 + 92)
= 2 x (4 + 92)
= 2 x 96
= 192 cm
2 Answer(s): (a) 21 : 3 : 1; (b) 192 cm
2