The rectangle is divided into four parts U, V, W and X. The ratio of Part U to Part V is 10 : 3 and the ratio of Part V to Part W is 3 : 1.
- Find the ratio of Part U to Part V to Part W.
- Given that Part X is 96 cm2 , find the area of the rectangle.
(a)
U |
V |
W |
X |
10x1 |
3x1 |
|
|
|
3x1 |
1x1 |
|
10 u |
3 u |
1 u |
96 cm2 |
Part V is the repeated identity.
LCM of 3 and 3 = 3
Part U : Part V : Part W = 10 : 3 : 1
(b)
Part U + Part V = Half of the rectangle
Part W + Part X = Half of the rectangle
Part U + Part V and Part W + Part X are equal.
Part U + Part V = Part W + Part X
10 u + 3 u = 1 u + 96
10 u + 3 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) 10 : 3 : 1; (b) 208 cm
2