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 1 : 3. The ratio of the area of R to the area of Q is 7 : 9. If the area of P is 325 cm
2, what is the area of the rectangle KLMN?
S |
R |
Q |
P |
1x7 |
3x7 |
|
|
|
7x3 |
9x3 |
|
7 u |
21 u |
27 u |
13 u |
Area R is the repeated identity.
LCM of 3 and 7 = 21
Half of the area of the rectangle
= Area S + Area Q
= 7 u + 27 u
= 34 u
Area of P
= Half of the area of the rectangle - Area R
= 34 u - 21 u
= 13 u
13 u = 325
1 u = 325 ÷ 13 = 25
Area of the rectangle
= 34 u x 2
= 68 u
= 68 x 25
= 1700 cm
2 Answer(s): 1700 cm
2