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 1 : 2. The ratio of the area of Q to the area of P is 4 : 5. If the area of N is 54 cm
2, what is the area of the rectangle JKLM?
R |
Q |
P |
N |
1x2 |
2x2 |
|
|
|
4x1 |
5x1 |
|
2 u |
4 u |
5 u |
3 u |
Area Q is the repeated identity.
LCM of 2 and 4 = 4
Half of the area of the rectangle
= Area R + Area P
= 2 u + 5 u
= 7 u
Area of N
= Half of the area of the rectangle - Area Q
= 7 u - 4 u
= 3 u
3 u = 54
1 u = 54 ÷ 3 = 18
Area of the rectangle
= 7 u x 2
= 14 u
= 14 x 18
= 252 cm
2 Answer(s): 252 cm
2