The figure, not drawn to scale, shows a rectangle, MNPQ, which is divided in 4 parts, R, S, T, and U. The ratio of the area of U to the area of T is 1 : 2. The ratio of the area of T to the area of S is 5 : 7. If the area of R is 162 cm
2, what is the area of the rectangle MNPQ?
U |
T |
S |
R |
1x5 |
2x5 |
|
|
|
5x2 |
7x2 |
|
5 u |
10 u |
14 u |
9 u |
Area T is the repeated identity.
LCM of 2 and 5 = 10
Half of the area of the rectangle
= Area U + Area S
= 5 u + 14 u
= 19 u
Area of R
= Half of the area of the rectangle - Area T
= 19 u - 10 u
= 9 u
9 u = 162
1 u = 162 ÷ 9 = 18
Area of the rectangle
= 19 u x 2
= 38 u
= 38 x 18
= 684 cm
2 Answer(s): 684 cm
2