The figure, not drawn to scale, shows a rectangle, LMNP, which is divided in 4 parts, Q, R, S, and T. The ratio of the area of T to the area of S is 2 : 5. The ratio of the area of S to the area of R is 9 : 10. If the area of Q is 368 cm
2, what is the area of the rectangle LMNP?
| T |
S |
R |
Q |
| 2x9 |
5x9 |
|
|
| |
9x5 |
10x5 |
|
| 18 u |
45 u |
50 u |
23 u |
Area S is the repeated identity.
LCM of 5 and 9 = 45
Half of the area of the rectangle
= Area T + Area R
= 18 u + 50 u
= 68 u
Area of Q
= Half of the area of the rectangle - Area S
= 68 u - 45 u
= 23 u
23 u = 368
1 u = 368 ÷ 23 = 16
Area of the rectangle
= 68 u x 2
= 136 u
= 136 x 16
= 2176 cm
2 Answer(s): 2176 cm
2 
