The figure, not drawn to scale, shows a rectangle, GHJK, which is divided in 4 parts, L, M, N, and P. The ratio of the area of P to the area of N is 2 : 5. The ratio of the area of N to the area of M is 9 : 10. If the area of L is 299 cm
2, what is the area of the rectangle GHJK?
P |
N |
M |
L |
2x9 |
5x9 |
|
|
|
9x5 |
10x5 |
|
18 u |
45 u |
50 u |
23 u |
Area N is the repeated identity.
LCM of 5 and 9 = 45
Half of the area of the rectangle
= Area P + Area M
= 18 u + 50 u
= 68 u
Area of L
= Half of the area of the rectangle - Area N
= 68 u - 45 u
= 23 u
23 u = 299
1 u = 299 ÷ 23 = 13
Area of the rectangle
= 68 u x 2
= 136 u
= 136 x 13
= 1768 cm
2 Answer(s): 1768 cm
2