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 2 : 5. The ratio of the area of T to the area of S is 4 : 5. If the area of R is 338 cm
2, what is the area of the rectangle MNPQ?
U |
T |
S |
R |
2x4 |
5x4 |
|
|
|
4x5 |
5x5 |
|
8 u |
20 u |
25 u |
13 u |
Area T is the repeated identity.
LCM of 5 and 4 = 20
Half of the area of the rectangle
= Area U + Area S
= 8 u + 25 u
= 33 u
Area of R
= Half of the area of the rectangle - Area T
= 33 u - 20 u
= 13 u
13 u = 338
1 u = 338 ÷ 13 = 26
Area of the rectangle
= 33 u x 2
= 66 u
= 66 x 26
= 1716 cm
2 Answer(s): 1716 cm
2