Question

A wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to its other end. How far from the base of the pole should the stake be driven so that the wire will be taut?

• A. $6\sqrt{10}m$
• B. $6\sqrt{7}m$
• C. $6\sqrt{2}m$
• D. $7\sqrt{6}m$

Answer 1

The correct option is B

$6\sqrt{7}m$

Let AB be the pole and AC be the wire.
From Pythagoras theorem,
$A{C}^2=A{B}^2+B{C}^2$
${24}^2={18}^2+B{C}^2$
$B{C}^2=576-324$
$B{C}^2=252$
$BC=6\sqrt{7}$ m
Therefore, the distance from the base is $6\sqrt{7}$ m.