The figure, not drawn to scale, shows a rectangle, LMNP, which is divided in 4 parts, Q, R, S, and T. The ratio of the area of T to the area of S is 2 : 7. The ratio of the area of S to the area of R is 9 : 10. If the area of Q is 400 cm
2, what is the area of the rectangle LMNP?
T |
S |
R |
Q |
2x9 |
7x9 |
|
|
|
9x7 |
10x7 |
|
18 u |
63 u |
70 u |
25 u |
Area S is the repeated identity.
LCM of 7 and 9 = 63
Half of the area of the rectangle
= Area T + Area R
= 18 u + 70 u
= 88 u
Area of Q
= Half of the area of the rectangle - Area S
= 88 u - 63 u
= 25 u
25 u = 400
1 u = 400 ÷ 25 = 16
Area of the rectangle
= 88 u x 2
= 176 u
= 176 x 16
= 2816 cm
2 Answer(s): 2816 cm
2