The figure, not drawn to scale, shows a rectangle, GHJK, which is divided in 4 parts, L, M, N, and P. The ratio of the area of P to the area of N is 2 : 5. The ratio of the area of N to the area of M is 8 : 9. If the area of L is 462 cm
2, what is the area of the rectangle GHJK?
P |
N |
M |
L |
2x8 |
5x8 |
|
|
|
8x5 |
9x5 |
|
16 u |
40 u |
45 u |
21 u |
Area N is the repeated identity.
LCM of 5 and 8 = 40
Half of the area of the rectangle
= Area P + Area M
= 16 u + 45 u
= 61 u
Area of L
= Half of the area of the rectangle - Area N
= 61 u - 40 u
= 21 u
21 u = 462
1 u = 462 ÷ 21 = 22
Area of the rectangle
= 61 u x 2
= 122 u
= 122 x 22
= 2684 cm
2 Answer(s): 2684 cm
2