Final answer:
Using similar triangles, the length of the shadow for the second pole of height 25√3 m is found to be 2505 m.
Step-by-step explanation:
The question is asking to find the length of the shadow cast by a pole of a different height given the length of the shadow of another pole and its height. This problem can be solved using similar triangles, as the pole and its shadow form a right triangle with the ground. Given the height of the first pole is 20 m and the shadow length is 2003 m, we can set up a ratio using the second pole's height, which is 25√3 m.
To find the second shadow length, we use the proportion:
First pole's height / First pole's shadow = Second pole's height / Second pole's shadow
20 / 2003 = 25√3 / x
Cross-multiplying gives us:
20x = 2003 * 25√3
Now solve for x:
x = (2003 * 25√3) / 20
Calculating the above expression gives:
x = 2505 m
Therefore, the length of the shadow of the pole of height 25√3 m is 2505 m, which corresponds to option A.