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 : 4. The ratio of the area of Q to the area of P is 7 : 8. If the area of N is 176 cm
2, what is the area of the rectangle JKLM?
R |
Q |
P |
N |
1x7 |
4x7 |
|
|
|
7x4 |
8x4 |
|
7 u |
28 u |
32 u |
11 u |
Area Q is the repeated identity.
LCM of 4 and 7 = 28
Half of the area of the rectangle
= Area R + Area P
= 7 u + 32 u
= 39 u
Area of N
= Half of the area of the rectangle - Area Q
= 39 u - 28 u
= 11 u
11 u = 176
1 u = 176 ÷ 11 = 16
Area of the rectangle
= 39 u x 2
= 78 u
= 78 x 16
= 1248 cm
2 Answer(s): 1248 cm
2