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 7 : 9. If the area of U is 600 cm
2, what is the area of the rectangle QRST?
X |
W |
V |
U |
2x7 |
5x7 |
|
|
|
7x5 |
9x5 |
|
14 u |
35 u |
45 u |
24 u |
Area W is the repeated identity.
LCM of 5 and 7 = 35
Half of the area of the rectangle
= Area X + Area V
= 14 u + 45 u
= 59 u
Area of U
= Half of the area of the rectangle - Area W
= 59 u - 35 u
= 24 u
24 u = 600
1 u = 600 ÷ 24 = 25
Area of the rectangle
= 59 u x 2
= 118 u
= 118 x 25
= 2950 cm
2 Answer(s): 2950 cm
2