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 1 : 3. The ratio of the area of W to the area of V is 6 : 7. If the area of U is 51 cm
2, what is the area of the rectangle QRST?
| X |
W |
V |
U |
| 1x2 |
3x2 |
|
|
| |
6x1 |
7x1 |
|
| 2 u |
6 u |
7 u |
3 u |
Area W is the repeated identity.
LCM of 3 and 6 = 6
Half of the area of the rectangle
= Area X + Area V
= 2 u + 7 u
= 9 u
Area of U
= Half of the area of the rectangle - Area W
= 9 u - 6 u
= 3 u
3 u = 51
1 u = 51 ÷ 3 = 17
Area of the rectangle
= 9 u x 2
= 18 u
= 18 x 17
= 306 cm
2 Answer(s): 306 cm
2 
