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.
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