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 4 : 5. If the area of N is 195 cm
2, what is the area of the rectangle JKLM?
R |
Q |
P |
N |
2x4 |
5x4 |
|
|
|
4x5 |
5x5 |
|
8 u |
20 u |
25 u |
13 u |
Area Q is the repeated identity.
LCM of 5 and 4 = 20
Half of the area of the rectangle
= Area R + Area P
= 8 u + 25 u
= 33 u
Area of N
= Half of the area of the rectangle - Area Q
= 33 u - 20 u
= 13 u
13 u = 195
1 u = 195 ÷ 13 = 15
Area of the rectangle
= 33 u x 2
= 66 u
= 66 x 15
= 990 cm
2 Answer(s): 990 cm
2