The figure, not drawn to scale, shows a rectangle, JKLM, which is divided in 4 parts, N, P, Q, and R. The ratio of the area of R to the area of Q is 2 : 7. The ratio of the area of Q to the area of P is 5 : 7. If the area of N is 456 cm
2, what is the area of the rectangle JKLM?
| R |
Q |
P |
N |
| 2x5 |
7x5 |
|
|
| |
5x7 |
7x7 |
|
| 10 u |
35 u |
49 u |
24 u |
Area Q is the repeated identity.
LCM of 7 and 5 = 35
Half of the area of the rectangle
= Area R + Area P
= 10 u + 49 u
= 59 u
Area of N
= Half of the area of the rectangle - Area Q
= 59 u - 35 u
= 24 u
24 u = 456
1 u = 456 ÷ 24 = 19
Area of the rectangle
= 59 u x 2
= 118 u
= 118 x 19
= 2242 cm
2 Answer(s): 2242 cm
2 
