The rectangle is divided into four parts T, U, V and W. The ratio of Part T to Part U is 10 : 1 and the ratio of Part U to Part V is 3 : 2.
- Find the ratio of Part T to Part U to Part V.
- Given that Part W is 93 m2 , find the area of the rectangle.
(a)
T |
U |
V |
W |
10x3 |
1x3 |
|
|
|
3x1 |
2x1 |
|
30 u |
3 u |
2 u |
93 m2 |
Part U is the repeated identity.
LCM of 1 and 3 = 3
Part T : Part U : Part V = 30 : 3 : 2
(b)
Part T + Part U = Half of the rectangle
Part V + Part W = Half of the rectangle
Part T + Part U and Part V + Part W are equal.
Part T + Part U = Part V + Part W
30 u + 3 u = 2 u + 93
30 u + 3 u - 2 u = 93
31 u = 93
1 u = 93 ÷ 31 = 3
Area of the rectangle
= 2 x (2 u + 93)
= 2 x (2 x 3 + 93)
= 2 x (6 + 93)
= 2 x 99
= 198 m
2 Answer(s): (a) 30 : 3 : 2; (b) 198 m
2