The straight line L of the figure divides the shadow area into three parts with an equal area.
Find the length of AB.
Find the length of AB.
Answer
One area equally divided into three is 60 / 3 = 20 cm2.
As shown in Fig. 1, draw the straight line passing through the center of this figure.
A trapezoid area in a figure can be calculated as 10 × (4 +4) = 80cm2.
Thus, CP = 20 / (18 - 14) = 5cm.
DQ = 20 / (8 - 6) =10 cm.
QR= 18 - 4/2 - 10 = 6 cm.
△BEP and △PRQ are homothetic and homothetic ratio is BE : PE = PR : QR = 2 : 6 = 1 : 3.
Thus, BE = 2 × 1/3 = 2/3.
Therefore, AB=5 - 2/3 = 13/3 cm.
13/3 cm
Solution
The total area of this figure is 18 × 8 - 14 × 6 = 60cm2.
One area equally divided into three is 60 / 3 = 20 cm2.
As shown in Fig. 1, draw the straight line passing through the center of this figure.
A trapezoid area in a figure can be calculated as 10 × (4 +4) = 80cm2.
Thus, CP = 20 / (18 - 14) = 5cm.
DQ = 20 / (8 - 6) =10 cm.
QR= 18 - 4/2 - 10 = 6 cm.
△BEP and △PRQ are homothetic and homothetic ratio is BE : PE = PR : QR = 2 : 6 = 1 : 3.
Thus, BE = 2 × 1/3 = 2/3.
Therefore, AB=5 - 2/3 = 13/3 cm.
