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 1 : 4. The ratio of the area of N to the area of M is 9 : 10. If the area of L is 351 cm
2, what is the area of the rectangle GHJK?
P |
N |
M |
L |
1x9 |
4x9 |
|
|
|
9x4 |
10x4 |
|
9 u |
36 u |
40 u |
13 u |
Area N is the repeated identity.
LCM of 4 and 9 = 36
Half of the area of the rectangle
= Area P + Area M
= 9 u + 40 u
= 49 u
Area of L
= Half of the area of the rectangle - Area N
= 49 u - 36 u
= 13 u
13 u = 351
1 u = 351 ÷ 13 = 27
Area of the rectangle
= 49 u x 2
= 98 u
= 98 x 27
= 2646 cm
2 Answer(s): 2646 cm
2