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 : 7. The ratio of the area of N to the area of M is 5 : 7. If the area of L is 720 cm
2, what is the area of the rectangle GHJK?
P |
N |
M |
L |
2x5 |
7x5 |
|
|
|
5x7 |
7x7 |
|
10 u |
35 u |
49 u |
24 u |
Area N is the repeated identity.
LCM of 7 and 5 = 35
Half of the area of the rectangle
= Area P + Area M
= 10 u + 49 u
= 59 u
Area of L
= Half of the area of the rectangle - Area N
= 59 u - 35 u
= 24 u
24 u = 720
1 u = 720 ÷ 24 = 30
Area of the rectangle
= 59 u x 2
= 118 u
= 118 x 30
= 3540 cm
2 Answer(s): 3540 cm
2