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 : 3. The ratio of the area of T to the area of S is 8 : 9. If the area of R is 143 cm
2, what is the area of the rectangle MNPQ?
U |
T |
S |
R |
1x8 |
3x8 |
|
|
|
8x3 |
9x3 |
|
8 u |
24 u |
27 u |
11 u |
Area T is the repeated identity.
LCM of 3 and 8 = 24
Half of the area of the rectangle
= Area U + Area S
= 8 u + 27 u
= 35 u
Area of R
= Half of the area of the rectangle - Area T
= 35 u - 24 u
= 11 u
11 u = 143
1 u = 143 ÷ 11 = 13
Area of the rectangle
= 35 u x 2
= 70 u
= 70 x 13
= 910 cm
2 Answer(s): 910 cm
2