The rectangle is divided into four parts L, M, N and P. The ratio of Part L to Part M is 7 : 5 and the ratio of Part M to Part N is 3 : 1.
- Find the ratio of Part L to Part M to Part N.
- Given that Part P is 31 cm2 , find the area of the rectangle.
(a)
L |
M |
N |
P |
7x3 |
5x3 |
|
|
|
3x5 |
1x5 |
|
21 u |
15 u |
5 u |
31 cm2 |
Part M is the repeated identity.
LCM of 5 and 3 = 15
Part L : Part M : Part N = 21 : 15 : 5
(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
21 u + 15 u = 5 u + 31
21 u + 15 u - 5 u = 31
31 u = 31
1 u = 31 ÷ 31 = 1
Area of the rectangle
= 2 x (5 u + 31)
= 2 x (5 x 1 + 31)
= 2 x (5 + 31)
= 2 x 36
= 72 cm
2 Answer(s): (a) 21 : 15 : 5; (b) 72 cm
2