Two poles of height 6m and 11m stands on a plane ground, if the distance between their feet is 12m. Find the distance between their tops.

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Answer: Two poles of height 6m and 11m stands on a plane ground, where distance between their feet is 12m, so the distance between the top of the two poles is 13 m.

The Pythagoras theorem works only for right-angled triangles. When any two values are known, we can apply the theorem and calculate the third side.

Explanation:

Let's draw the diagram of the two poles AB and CD as shown:

Let, BD be the distance between the top of the two poles.

Assume, BD = x meters

As △BED is a right-angled triangle, right angled at E, therefore 'x' is the hypotenuse.

Now apply the Pythagoras theorem on △BED ,

Hypotenuse² = Perpendicular² + Base²

⇒ BD² = ED² + BE²

⇒ x² = 12² + 5²

⇒ x² = 144 + 25

⇒ x² = 169

⇒ x = 13 m

Therefore, the distance between the top of the two poles is 13 m.