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 5 : 7. If the area of R is 286 cm
2, what is the area of the rectangle MNPQ?
U |
T |
S |
R |
1x5 |
3x5 |
|
|
|
5x3 |
7x3 |
|
5 u |
15 u |
21 u |
11 u |
Area T is the repeated identity.
LCM of 3 and 5 = 15
Half of the area of the rectangle
= Area U + Area S
= 5 u + 21 u
= 26 u
Area of R
= Half of the area of the rectangle - Area T
= 26 u - 15 u
= 11 u
11 u = 286
1 u = 286 ÷ 11 = 26
Area of the rectangle
= 26 u x 2
= 52 u
= 52 x 26
= 1352 cm
2 Answer(s): 1352 cm
2