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 : 2. The ratio of the area of W to the area of V is 4 : 5. If the area of U is 66 cm
2, what is the area of the rectangle QRST?
X |
W |
V |
U |
1x2 |
2x2 |
|
|
|
4x1 |
5x1 |
|
2 u |
4 u |
5 u |
3 u |
Area W is the repeated identity.
LCM of 2 and 4 = 4
Half of the area of the rectangle
= Area X + Area V
= 2 u + 5 u
= 7 u
Area of U
= Half of the area of the rectangle - Area W
= 7 u - 4 u
= 3 u
3 u = 66
1 u = 66 ÷ 3 = 22
Area of the rectangle
= 7 u x 2
= 14 u
= 14 x 22
= 308 cm
2 Answer(s): 308 cm
2