The figure, not drawn to scale, shows a rectangle, PQRS, which is divided in 4 parts, T, U, V, and W. The ratio of the area of W to the area of V is 2 : 7. The ratio of the area of V to the area of U is 6 : 7. If the area of T is 228 cm
2, what is the area of the rectangle PQRS?
W |
V |
U |
T |
2x6 |
7x6 |
|
|
|
6x7 |
7x7 |
|
12 u |
42 u |
49 u |
19 u |
Area V is the repeated identity.
LCM of 7 and 6 = 42
Half of the area of the rectangle
= Area W + Area U
= 12 u + 49 u
= 61 u
Area of T
= Half of the area of the rectangle - Area V
= 61 u - 42 u
= 19 u
19 u = 228
1 u = 228 ÷ 19 = 12
Area of the rectangle
= 61 u x 2
= 122 u
= 122 x 12
= 1464 cm
2 Answer(s): 1464 cm
2