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 4 : 1.
- Find the ratio of Part U to Part V to Part W.
- Given that Part X is 30 cm2 , find the area of the rectangle.
(a)
U |
V |
W |
X |
7x1 |
4x1 |
|
|
|
4x1 |
1x1 |
|
7 u |
4 u |
1 u |
30 cm2 |
Part V is the repeated identity.
LCM of 4 and 4 = 4
Part U : Part V : Part W = 7 : 4 : 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
7 u + 4 u = 1 u + 30
7 u + 4 u - 1 u = 30
10 u = 30
1 u = 30 ÷ 10 = 3
Area of the rectangle
= 2 x (1 u + 30)
= 2 x (1 x 3 + 30)
= 2 x (3 + 30)
= 2 x 33
= 66 cm
2 Answer(s): (a) 7 : 4 : 1; (b) 66 cm
2