The rectangle is divided into four parts J, K, L and M. The ratio of Part J to Part K is 9 : 5 and the ratio of Part K to Part L is 3 : 2.
- Find the ratio of Part J to Part K to Part L.
- Given that Part M is 32 cm2 , find the area of the rectangle.
(a)
J |
K |
L |
M |
9x3 |
5x3 |
|
|
|
3x5 |
2x5 |
|
27 u |
15 u |
10 u |
32 cm2 |
Part K is the repeated identity.
LCM of 5 and 3 = 15
Part J : Part K : Part L = 27 : 15 : 10
(b)
Part J + Part K = Half of the rectangle
Part L + Part M = Half of the rectangle
Part J + Part K and Part L + Part M are equal.
Part J + Part K = Part L + Part M
27 u + 15 u = 10 u + 32
27 u + 15 u - 10 u = 32
32 u = 32
1 u = 32 ÷ 32 = 1
Area of the rectangle
= 2 x (10 u + 32)
= 2 x (10 x 1 + 32)
= 2 x (10 + 32)
= 2 x 42
= 84 cm
2 Answer(s): (a) 27 : 15 : 10; (b) 84 cm
2