The figure, not drawn to scale, shows a rectangle, KLMN, which is divided in 4 parts, P, Q, R, and S. The ratio of the area of S to the area of R is 2 : 7. The ratio of the area of R to the area of Q is 5 : 7. If the area of P is 624 cm
2, what is the area of the rectangle KLMN?
S |
R |
Q |
P |
2x5 |
7x5 |
|
|
|
5x7 |
7x7 |
|
10 u |
35 u |
49 u |
24 u |
Area R is the repeated identity.
LCM of 7 and 5 = 35
Half of the area of the rectangle
= Area S + Area Q
= 10 u + 49 u
= 59 u
Area of P
= Half of the area of the rectangle - Area R
= 59 u - 35 u
= 24 u
24 u = 624
1 u = 624 ÷ 24 = 26
Area of the rectangle
= 59 u x 2
= 118 u
= 118 x 26
= 3068 cm
2 Answer(s): 3068 cm
2