Two vertical poles of height 9 m and 14 m stand on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.

Let BC and AD be the two poles of height 14m and 9m respectively. Again, let CD be the distance between tops of the poles.

Then, CE = BC – AD = 14 – 9 = 5m [∵AD =BE]

Also, AB =12m

In ∆CED, using Pythagoras theorem, we get

(Perpendicular)² + (Base)² = (Hypotenuse)²

⇒ (CE)² + (DE)² = (CD)²

⇒ (5)² + (12)² = (CD)²

⇒ (CD)² = 25 + 144

⇒ (CD)² = 169

⇒ CD = √169

⇒ CD = ±13

⇒ CD = 13 [taking positive square root]

Hence, the distance between the tops of the poles is 13m