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 : 7. The ratio of the area of W to the area of V is 5 : 6. If the area of U is 493 cm
2, what is the area of the rectangle QRST?
X |
W |
V |
U |
2x5 |
7x5 |
|
|
|
5x7 |
6x7 |
|
10 u |
35 u |
42 u |
17 u |
Area W is the repeated identity.
LCM of 7 and 5 = 35
Half of the area of the rectangle
= Area X + Area V
= 10 u + 42 u
= 52 u
Area of U
= Half of the area of the rectangle - Area W
= 52 u - 35 u
= 17 u
17 u = 493
1 u = 493 ÷ 17 = 29
Area of the rectangle
= 52 u x 2
= 104 u
= 104 x 29
= 3016 cm
2 Answer(s): 3016 cm
2