The figure, not drawn to scale, shows a rectangle, QRST, which is divided in 4 parts, U, V, W, and X. The ratio of the area of X to the area of W is 2 : 5. The ratio of the area of W to the area of V is 6 : 7. If the area of U is 476 cm
2, what is the area of the rectangle QRST?
X |
W |
V |
U |
2x6 |
5x6 |
|
|
|
6x5 |
7x5 |
|
12 u |
30 u |
35 u |
17 u |
Area W is the repeated identity.
LCM of 5 and 6 = 30
Half of the area of the rectangle
= Area X + Area V
= 12 u + 35 u
= 47 u
Area of U
= Half of the area of the rectangle - Area W
= 47 u - 30 u
= 17 u
17 u = 476
1 u = 476 ÷ 17 = 28
Area of the rectangle
= 47 u x 2
= 94 u
= 94 x 28
= 2632 cm
2 Answer(s): 2632 cm
2