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 : 5. The ratio of the area of R to the area of Q is 4 : 5. If the area of P is 221 cm
2, what is the area of the rectangle KLMN?
S |
R |
Q |
P |
2x4 |
5x4 |
|
|
|
4x5 |
5x5 |
|
8 u |
20 u |
25 u |
13 u |
Area R is the repeated identity.
LCM of 5 and 4 = 20
Half of the area of the rectangle
= Area S + Area Q
= 8 u + 25 u
= 33 u
Area of P
= Half of the area of the rectangle - Area R
= 33 u - 20 u
= 13 u
13 u = 221
1 u = 221 ÷ 13 = 17
Area of the rectangle
= 33 u x 2
= 66 u
= 66 x 17
= 1122 cm
2 Answer(s): 1122 cm
2