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 7 : 8. If the area of N is 234 cm
2, what is the area of the rectangle JKLM?
R |
Q |
P |
N |
1x7 |
2x7 |
|
|
|
7x2 |
8x2 |
|
7 u |
14 u |
16 u |
9 u |
Area Q is the repeated identity.
LCM of 2 and 7 = 14
Half of the area of the rectangle
= Area R + Area P
= 7 u + 16 u
= 23 u
Area of N
= Half of the area of the rectangle - Area Q
= 23 u - 14 u
= 9 u
9 u = 234
1 u = 234 ÷ 9 = 26
Area of the rectangle
= 23 u x 2
= 46 u
= 46 x 26
= 1196 cm
2 Answer(s): 1196 cm
2