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 : 3. The ratio of the area of Q to the area of P is 7 : 8. If the area of N is 270 cm
2, what is the area of the rectangle JKLM?
R |
Q |
P |
N |
1x7 |
3x7 |
|
|
|
7x3 |
8x3 |
|
7 u |
21 u |
24 u |
10 u |
Area Q is the repeated identity.
LCM of 3 and 7 = 21
Half of the area of the rectangle
= Area R + Area P
= 7 u + 24 u
= 31 u
Area of N
= Half of the area of the rectangle - Area Q
= 31 u - 21 u
= 10 u
10 u = 270
1 u = 270 ÷ 10 = 27
Area of the rectangle
= 31 u x 2
= 62 u
= 62 x 27
= 1674 cm
2 Answer(s): 1674 cm
2