The rectangle is divided into four parts R, S, T and U. The ratio of Part R to Part S is 9 : 4 and the ratio of Part S to Part T is 4 : 1.
- Find the ratio of Part R to Part S to Part T.
- Given that Part U is 96 cm2 , find the area of the rectangle.
(a)
R |
S |
T |
U |
9x1 |
4x1 |
|
|
|
4x1 |
1x1 |
|
9 u |
4 u |
1 u |
96 cm2 |
Part S is the repeated identity.
LCM of 4 and 4 = 4
Part R : Part S : Part T = 9 : 4 : 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
9 u + 4 u = 1 u + 96
9 u + 4 u - 1 u = 96
12 u = 96
1 u = 96 ÷ 12 = 8
Area of the rectangle
= 2 x (1 u + 96)
= 2 x (1 x 8 + 96)
= 2 x (8 + 96)
= 2 x 104
= 208 cm
2 Answer(s): (a) 9 : 4 : 1; (b) 208 cm
2