The rectangle is divided into four parts R, S, T and U. The ratio of Part R to Part S is 7 : 2 and the ratio of Part S to Part T is 4 : 1.
- Find the ratio of Part R to Part S to Part T.
- Given that Part U is 17 cm2 , find the area of the rectangle.
(a)
R |
S |
T |
U |
7x2 |
2x2 |
|
|
|
4x1 |
1x1 |
|
14 u |
4 u |
1 u |
17 cm2 |
Part S is the repeated identity.
LCM of 2 and 4 = 4
Part R : Part S : Part T = 14 : 4 : 1
(b)
Part R + Part S = Half of the rectangle
Part T + Part U = Half of the rectangle
Part R + Part S and Part T + Part U are equal.
Part R + Part S = Part T + Part U
14 u + 4 u = 1 u + 17
14 u + 4 u - 1 u = 17
17 u = 17
1 u = 17 ÷ 17 = 1
Area of the rectangle
= 2 x (1 u + 17)
= 2 x (1 x 1 + 17)
= 2 x (1 + 17)
= 2 x 18
= 36 cm
2 Answer(s): (a) 14 : 4 : 1; (b) 36 cm
2