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 8 : 9. If the area of N is 75 cm
2, what is the area of the rectangle JKLM?
R |
Q |
P |
N |
1x4 |
2x4 |
|
|
|
8x1 |
9x1 |
|
4 u |
8 u |
9 u |
5 u |
Area Q is the repeated identity.
LCM of 2 and 8 = 8
Half of the area of the rectangle
= Area R + Area P
= 4 u + 9 u
= 13 u
Area of N
= Half of the area of the rectangle - Area Q
= 13 u - 8 u
= 5 u
5 u = 75
1 u = 75 ÷ 5 = 15
Area of the rectangle
= 13 u x 2
= 26 u
= 26 x 15
= 390 cm
2 Answer(s): 390 cm
2