Question

The length of the shadow of a pole, having a height of 20 m, is 2003 m. Find the length of the shadow of a pole of height (25√{3}) m at the same time.

A. 2505 m
B. 2418 m
C. 2257 m
D. 2115 m

Answer 1

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.