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 8 : 9. If the area of R is 115 cm
2, what is the area of the rectangle MNPQ?
U |
T |
S |
R |
1x4 |
2x4 |
|
|
|
8x1 |
9x1 |
|
4 u |
8 u |
9 u |
5 u |
Area T is the repeated identity.
LCM of 2 and 8 = 8
Half of the area of the rectangle
= Area U + Area S
= 4 u + 9 u
= 13 u
Area of R
= Half of the area of the rectangle - Area T
= 13 u - 8 u
= 5 u
5 u = 115
1 u = 115 ÷ 5 = 23
Area of the rectangle
= 13 u x 2
= 26 u
= 26 x 23
= 598 cm
2 Answer(s): 598 cm
2