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 5 : 6. If the area of U is 175 cm
2, what is the area of the rectangle QRST?
X |
W |
V |
U |
1x5 |
2x5 |
|
|
|
5x2 |
6x2 |
|
5 u |
10 u |
12 u |
7 u |
Area W is the repeated identity.
LCM of 2 and 5 = 10
Half of the area of the rectangle
= Area X + Area V
= 5 u + 12 u
= 17 u
Area of U
= Half of the area of the rectangle - Area W
= 17 u - 10 u
= 7 u
7 u = 175
1 u = 175 ÷ 7 = 25
Area of the rectangle
= 17 u x 2
= 34 u
= 34 x 25
= 850 cm
2 Answer(s): 850 cm
2