The figure, not drawn to scale, shows a rectangle, JKLM, which is divided in 4 parts, N, P, Q, and R. The ratio of the area of R to the area of Q is 2 : 5. The ratio of the area of Q to the area of P is 9 : 10. If the area of N is 276 cm
2, what is the area of the rectangle JKLM?
R |
Q |
P |
N |
2x9 |
5x9 |
|
|
|
9x5 |
10x5 |
|
18 u |
45 u |
50 u |
23 u |
Area Q is the repeated identity.
LCM of 5 and 9 = 45
Half of the area of the rectangle
= Area R + Area P
= 18 u + 50 u
= 68 u
Area of N
= Half of the area of the rectangle - Area Q
= 68 u - 45 u
= 23 u
23 u = 276
1 u = 276 ÷ 23 = 12
Area of the rectangle
= 68 u x 2
= 136 u
= 136 x 12
= 1632 cm
2 Answer(s): 1632 cm
2