The rectangle is divided into four parts U, V, W and X. The ratio of Part U to Part V is 7 : 4 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 87 cm2 , find the area of the rectangle.
(a)
U |
V |
W |
X |
7x3 |
4x3 |
|
|
|
3x4 |
1x4 |
|
21 u |
12 u |
4 u |
87 cm2 |
Part V is the repeated identity.
LCM of 4 and 3 = 12
Part U : Part V : Part W = 21 : 12 : 4
(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
21 u + 12 u = 4 u + 87
21 u + 12 u - 4 u = 87
29 u = 87
1 u = 87 ÷ 29 = 3
Area of the rectangle
= 2 x (4 u + 87)
= 2 x (4 x 3 + 87)
= 2 x (12 + 87)
= 2 x 99
= 198 cm
2 Answer(s): (a) 21 : 12 : 4; (b) 198 cm
2