The rectangle is divided into four parts J, K, L and M. The ratio of Part J to Part K is 8 : 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 58 m2 , find the area of the rectangle.
(a)
J |
K |
L |
M |
8x3 |
5x3 |
|
|
|
3x5 |
2x5 |
|
24 u |
15 u |
10 u |
58 m2 |
Part K is the repeated identity.
LCM of 5 and 3 = 15
Part J : Part K : Part L = 24 : 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
24 u + 15 u = 10 u + 58
24 u + 15 u - 10 u = 58
29 u = 58
1 u = 58 ÷ 29 = 2
Area of the rectangle
= 2 x (10 u + 58)
= 2 x (10 x 2 + 58)
= 2 x (20 + 58)
= 2 x 78
= 156 m
2 Answer(s): (a) 24 : 15 : 10; (b) 156 m
2