The rectangle is divided into four parts L, M, N and P. The ratio of Part L to Part M is 8 : 3 and the ratio of Part M to Part N is 4 : 1.
- Find the ratio of Part L to Part M to Part N.
- Given that Part P is 82 cm2 , find the area of the rectangle.
(a)
L |
M |
N |
P |
8x4 |
3x4 |
|
|
|
4x3 |
1x3 |
|
32 u |
12 u |
3 u |
82 cm2 |
Part M is the repeated identity.
LCM of 3 and 4 = 12
Part L : Part M : Part N = 32 : 12 : 3
(b)
Part L + Part M = Half of the rectangle
Part N + Part P = Half of the rectangle
Part L + Part M and Part N + Part P are equal.
Part L + Part M = Part N + Part P
32 u + 12 u = 3 u + 82
32 u + 12 u - 3 u = 82
41 u = 82
1 u = 82 ÷ 41 = 2
Area of the rectangle
= 2 x (3 u + 82)
= 2 x (3 x 2 + 82)
= 2 x (6 + 82)
= 2 x 88
= 176 cm
2 Answer(s): (a) 32 : 12 : 3; (b) 176 cm
2