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 5 : 7. If the area of Q is 377 cm
2, what is the area of the rectangle LMNP?
T |
S |
R |
Q |
1x5 |
4x5 |
|
|
|
5x4 |
7x4 |
|
5 u |
20 u |
28 u |
13 u |
Area S is the repeated identity.
LCM of 4 and 5 = 20
Half of the area of the rectangle
= Area T + Area R
= 5 u + 28 u
= 33 u
Area of Q
= Half of the area of the rectangle - Area S
= 33 u - 20 u
= 13 u
13 u = 377
1 u = 377 ÷ 13 = 29
Area of the rectangle
= 33 u x 2
= 66 u
= 66 x 29
= 1914 cm
2 Answer(s): 1914 cm
2