The rectangle is divided into four parts R, S, T and U. The ratio of Part R to Part S is 8 : 5 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 94 m2 , find the area of the rectangle.
(a)
R |
S |
T |
U |
8x4 |
5x4 |
|
|
|
4x5 |
1x5 |
|
32 u |
20 u |
5 u |
94 m2 |
Part S is the repeated identity.
LCM of 5 and 4 = 20
Part R : Part S : Part T = 32 : 20 : 5
(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
32 u + 20 u = 5 u + 94
32 u + 20 u - 5 u = 94
47 u = 94
1 u = 94 ÷ 47 = 2
Area of the rectangle
= 2 x (5 u + 94)
= 2 x (5 x 2 + 94)
= 2 x (10 + 94)
= 2 x 104
= 208 m
2 Answer(s): (a) 32 : 20 : 5; (b) 208 m
2