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 9 : 10. If the area of P is 575 cm
2, what is the area of the rectangle KLMN?
S |
R |
Q |
P |
2x9 |
7x9 |
|
|
|
9x7 |
10x7 |
|
18 u |
63 u |
70 u |
25 u |
Area R is the repeated identity.
LCM of 7 and 9 = 63
Half of the area of the rectangle
= Area S + Area Q
= 18 u + 70 u
= 88 u
Area of P
= Half of the area of the rectangle - Area R
= 88 u - 63 u
= 25 u
25 u = 575
1 u = 575 ÷ 25 = 23
Area of the rectangle
= 88 u x 2
= 176 u
= 176 x 23
= 4048 cm
2 Answer(s): 4048 cm
2