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 1 : 3. The ratio of the area of S to the area of R is 7 : 9. If the area of Q is 273 cm
2, what is the area of the rectangle LMNP?
T |
S |
R |
Q |
1x7 |
3x7 |
|
|
|
7x3 |
9x3 |
|
7 u |
21 u |
27 u |
13 u |
Area S is the repeated identity.
LCM of 3 and 7 = 21
Half of the area of the rectangle
= Area T + Area R
= 7 u + 27 u
= 34 u
Area of Q
= Half of the area of the rectangle - Area S
= 34 u - 21 u
= 13 u
13 u = 273
1 u = 273 ÷ 13 = 21
Area of the rectangle
= 34 u x 2
= 68 u
= 68 x 21
= 1428 cm
2 Answer(s): 1428 cm
2