The rectangle is divided into four parts S, T, U and V. The ratio of Part S to Part T is 7 : 4 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 25 m2 , find the area of the rectangle.
(a)
S |
T |
U |
V |
7x3 |
4x3 |
|
|
|
3x4 |
2x4 |
|
21 u |
12 u |
8 u |
25 m2 |
Part T is the repeated identity.
LCM of 4 and 3 = 12
Part S : Part T : Part U = 21 : 12 : 8
(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
21 u + 12 u = 8 u + 25
21 u + 12 u - 8 u = 25
25 u = 25
1 u = 25 ÷ 25 = 1
Area of the rectangle
= 2 x (8 u + 25)
= 2 x (8 x 1 + 25)
= 2 x (8 + 25)
= 2 x 33
= 66 m
2 Answer(s): (a) 21 : 12 : 8; (b) 66 m
2