The rectangle is divided into four parts S, T, U and V. The ratio of Part S to Part T is 9 : 1 and the ratio of Part T to Part U is 3 : 2.
- Find the ratio of Part S to Part T to Part U.
- Given that Part V is 28 cm2 , find the area of the rectangle.
(a)
S |
T |
U |
V |
9x3 |
1x3 |
|
|
|
3x1 |
2x1 |
|
27 u |
3 u |
2 u |
28 cm2 |
Part T is the repeated identity.
LCM of 1 and 3 = 3
Part S : Part T : Part U = 27 : 3 : 2
(b)
Part S + Part T = Half of the rectangle
Part U + Part V = Half of the rectangle
Part S + Part T and Part U + Part V are equal.
Part S + Part T = Part U + Part V
27 u + 3 u = 2 u + 28
27 u + 3 u - 2 u = 28
28 u = 28
1 u = 28 ÷ 28 = 1
Area of the rectangle
= 2 x (2 u + 28)
= 2 x (2 x 1 + 28)
= 2 x (2 + 28)
= 2 x 30
= 60 cm
2 Answer(s): (a) 27 : 3 : 2; (b) 60 cm
2