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Answer:
The length of the shadow is increasing with the rate of 1.5 feet per sec
Step-by-step explanation:
Let AB and CD represents the height of the lamppost and child respectively ( shown below )
Also, let E be a point represents the position of child.
In triangles ABE and CDE,
( right angles )
( common angles )
By AA similarity postulate,
∵ Corresponding sides of similar triangles are in same proportion,
We have, AB = 12 ft, CD = 4 ft, BE = BD + DE = 6 + DE,
Now, the speed of walking = 2 mph =
Note: 1 mile = 5280 ft, 1 hour = 3600 sec
Thus, the time taken by child to reach at E
= 2.045 hours
Hence, the change rate in the length of shadow
= 1.5 ft per sec.
