Question

Two poles of height, 20 ft and 30 ft are standing at a distance of 10 ft from each other. Find the distance between the tops of these poles.

• A. $10ft$
• B. $10\sqrt{2}ft$
• C. $10\sqrt{3}ft$
• D. $5\sqrt{2}ft$

Answer 1

The correct option is B $10\sqrt{2}ft$

We can find the distance between the tops of poles using Pythagors' theorem.

Let's draw perpendicular from top of the smaller pole to larger pole.

As we can see that distance between tops of poles is nothing but hypotenuse of right -angled triangle.

Using Pythagoras' Theorem,

${\text{(Hypotenuse)}}^2={\text{(Base)}}^2+{\text{(Height)}}^2$

${\text{(Hypotenuse)}}^2={10}^2+{10}^2$

${\text{(Hypotenuse)}}^2=100+100$

${\text{(Hypotenuse)}}^2=200$

$\text{(Hypotenuse)}=10\sqrt{2}ft$