tow pols of haights between 6meter and 11meter stand on a plane graund .if the distanse between the feet of the poles 12 meter .the distanse their tops equal to

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Assuming one pole has height 6 and the other has height 11, then the distance between their tops is just

√(12^2+5^2) = 13 meters

To find the distance between the tops of the poles, we can use the concept of similar triangles.

Let's assume the height of the shorter pole is x meters.

Since we are given that the distance between the feet of the poles is 12 meters, and we know the heights of the poles are 6 meters and x meters respectively, we can set up the following proportion:

6/12 = x/(x+5)

We can now solve for x by cross-multiplying and simplifying the equation:

6(x+5) = 12x

6x + 30 = 12x

30 = 12x - 6x

30 = 6x

Dividing both sides by 6:

x = 5

Therefore, the height of the shorter pole is 5 meters.

Now that we know the height of the shorter pole, we can calculate the height of the taller pole by using the given information that the distance between the tops of the poles is the same as the distance between the feet.

Let's assume the height of the taller pole is y meters.

Using the same proportion as before, we have:

6/12 = y/(y+5)

Solving for y in the equation:

6(y+5) = 12y

6y + 30 = 12y

30 = 12y - 6y

30 = 6y

Dividing both sides by 6:

y = 5

Therefore, the height of the taller pole is 5 meters.

Hence, the distance between the tops of the poles is equal to the height of the shorter pole plus the height of the taller pole:

Distance = 5 + 5 = 10 meters.