The rectangle is divided into four parts T, U, V and W. The ratio of Part T to Part U is 8 : 1 and the ratio of Part U to Part V is 3 : 1.
- Find the ratio of Part T to Part U to Part V.
- Given that Part W is 26 cm2 , find the area of the rectangle.
(a)
T |
U |
V |
W |
8x3 |
1x3 |
|
|
|
3x1 |
1x1 |
|
24 u |
3 u |
1 u |
26 cm2 |
Part U is the repeated identity.
LCM of 1 and 3 = 3
Part T : Part U : Part V = 24 : 3 : 1
(b)
Part T + Part U = Half of the rectangle
Part V + Part W = Half of the rectangle
Part T + Part U and Part V + Part W are equal.
Part T + Part U = Part V + Part W
24 u + 3 u = 1 u + 26
24 u + 3 u - 1 u = 26
26 u = 26
1 u = 26 ÷ 26 = 1
Area of the rectangle
= 2 x (1 u + 26)
= 2 x (1 x 1 + 26)
= 2 x (1 + 26)
= 2 x 27
= 54 cm
2 Answer(s): (a) 24 : 3 : 1; (b) 54 cm
2