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 : 4. The ratio of the area of S to the area of R is 6 : 7. If the area of Q is 60 cm
2, what is the area of the rectangle LMNP?
T |
S |
R |
Q |
1x3 |
4x3 |
|
|
|
6x2 |
7x2 |
|
3 u |
12 u |
14 u |
5 u |
Area S is the repeated identity.
LCM of 4 and 6 = 12
Half of the area of the rectangle
= Area T + Area R
= 3 u + 14 u
= 17 u
Area of Q
= Half of the area of the rectangle - Area S
= 17 u - 12 u
= 5 u
5 u = 60
1 u = 60 ÷ 5 = 12
Area of the rectangle
= 17 u x 2
= 34 u
= 34 x 12
= 408 cm
2 Answer(s): 408 cm
2