The rectangle is divided into four parts S, T, U and V. The ratio of Part S to Part T is 8 : 3 and the ratio of Part T to Part U is 3 : 1.
- Find the ratio of Part S to Part T to Part U.
- Given that Part V is 40 cm2 , find the area of the rectangle.
(a)
S |
T |
U |
V |
8x1 |
3x1 |
|
|
|
3x1 |
1x1 |
|
8 u |
3 u |
1 u |
40 cm2 |
Part T is the repeated identity.
LCM of 3 and 3 = 3
Part S : Part T : Part U = 8 : 3 : 1
(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
8 u + 3 u = 1 u + 40
8 u + 3 u - 1 u = 40
10 u = 40
1 u = 40 ÷ 10 = 4
Area of the rectangle
= 2 x (1 u + 40)
= 2 x (1 x 4 + 40)
= 2 x (4 + 40)
= 2 x 44
= 88 cm
2 Answer(s): (a) 8 : 3 : 1; (b) 88 cm
2