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 9 : 10. If the area of P is 112 cm
2, what is the area of the rectangle KLMN?
S |
R |
Q |
P |
1x3 |
3x3 |
|
|
|
9x1 |
10x1 |
|
3 u |
9 u |
10 u |
4 u |
Area R is the repeated identity.
LCM of 3 and 9 = 9
Half of the area of the rectangle
= Area S + Area Q
= 3 u + 10 u
= 13 u
Area of P
= Half of the area of the rectangle - Area R
= 13 u - 9 u
= 4 u
4 u = 112
1 u = 112 ÷ 4 = 28
Area of the rectangle
= 13 u x 2
= 26 u
= 26 x 28
= 728 cm
2 Answer(s): 728 cm
2