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 8 : 9. If the area of N is 399 cm
2, what is the area of the rectangle JKLM?
R |
Q |
P |
N |
2x8 |
5x8 |
|
|
|
8x5 |
9x5 |
|
16 u |
40 u |
45 u |
21 u |
Area Q is the repeated identity.
LCM of 5 and 8 = 40
Half of the area of the rectangle
= Area R + Area P
= 16 u + 45 u
= 61 u
Area of N
= Half of the area of the rectangle - Area Q
= 61 u - 40 u
= 21 u
21 u = 399
1 u = 399 ÷ 21 = 19
Area of the rectangle
= 61 u x 2
= 122 u
= 122 x 19
= 2318 cm
2 Answer(s): 2318 cm
2