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 1 : 2. The ratio of the area of V to the area of U is 8 : 9. If the area of T is 80 cm
2, what is the area of the rectangle PQRS?
W |
V |
U |
T |
1x4 |
2x4 |
|
|
|
8x1 |
9x1 |
|
4 u |
8 u |
9 u |
5 u |
Area V is the repeated identity.
LCM of 2 and 8 = 8
Half of the area of the rectangle
= Area W + Area U
= 4 u + 9 u
= 13 u
Area of T
= Half of the area of the rectangle - Area V
= 13 u - 8 u
= 5 u
5 u = 80
1 u = 80 ÷ 5 = 16
Area of the rectangle
= 13 u x 2
= 26 u
= 26 x 16
= 416 cm
2 Answer(s): 416 cm
2