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 : 8. If the area of Q is 220 cm
2, what is the area of the rectangle LMNP?
T |
S |
R |
Q |
1x7 |
3x7 |
|
|
|
7x3 |
8x3 |
|
7 u |
21 u |
24 u |
10 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 + 24 u
= 31 u
Area of Q
= Half of the area of the rectangle - Area S
= 31 u - 21 u
= 10 u
10 u = 220
1 u = 220 ÷ 10 = 22
Area of the rectangle
= 31 u x 2
= 62 u
= 62 x 22
= 1364 cm
2 Answer(s): 1364 cm
2