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 : 7. The ratio of the area of Q to the area of P is 4 : 5. If the area of N is 210 cm
2, what is the area of the rectangle JKLM?
R |
Q |
P |
N |
2x4 |
7x4 |
|
|
|
4x7 |
5x7 |
|
8 u |
28 u |
35 u |
15 u |
Area Q is the repeated identity.
LCM of 7 and 4 = 28
Half of the area of the rectangle
= Area R + Area P
= 8 u + 35 u
= 43 u
Area of N
= Half of the area of the rectangle - Area Q
= 43 u - 28 u
= 15 u
15 u = 210
1 u = 210 ÷ 15 = 14
Area of the rectangle
= 43 u x 2
= 86 u
= 86 x 14
= 1204 cm
2 Answer(s): 1204 cm
2