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 : 2. The ratio of the area of S to the area of R is 4 : 5. If the area of Q is 39 cm
2, what is the area of the rectangle LMNP?
T |
S |
R |
Q |
1x2 |
2x2 |
|
|
|
4x1 |
5x1 |
|
2 u |
4 u |
5 u |
3 u |
Area S is the repeated identity.
LCM of 2 and 4 = 4
Half of the area of the rectangle
= Area T + Area R
= 2 u + 5 u
= 7 u
Area of Q
= Half of the area of the rectangle - Area S
= 7 u - 4 u
= 3 u
3 u = 39
1 u = 39 ÷ 3 = 13
Area of the rectangle
= 7 u x 2
= 14 u
= 14 x 13
= 182 cm
2 Answer(s): 182 cm
2