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 7 : 8. If the area of Q is 380 cm
2, what is the area of the rectangle LMNP?
| T |
S |
R |
Q |
| 2x7 |
5x7 |
|
|
| |
7x5 |
8x5 |
|
| 14 u |
35 u |
40 u |
19 u |
Area S is the repeated identity.
LCM of 5 and 7 = 35
Half of the area of the rectangle
= Area T + Area R
= 14 u + 40 u
= 54 u
Area of Q
= Half of the area of the rectangle - Area S
= 54 u - 35 u
= 19 u
19 u = 380
1 u = 380 ÷ 19 = 20
Area of the rectangle
= 54 u x 2
= 108 u
= 108 x 20
= 2160 cm
2 Answer(s): 2160 cm
2 
