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 6 : 7. If the area of U is 80 cm
2, what is the area of the rectangle QRST?
X |
W |
V |
U |
1x3 |
2x3 |
|
|
|
6x1 |
7x1 |
|
3 u |
6 u |
7 u |
4 u |
Area W is the repeated identity.
LCM of 2 and 6 = 6
Half of the area of the rectangle
= Area X + Area V
= 3 u + 7 u
= 10 u
Area of U
= Half of the area of the rectangle - Area W
= 10 u - 6 u
= 4 u
4 u = 80
1 u = 80 ÷ 4 = 20
Area of the rectangle
= 10 u x 2
= 20 u
= 20 x 20
= 400 cm
2 Answer(s): 400 cm
2