Let us find the length of rope Jules will need using the pythagoras theorem .
Width of the moat ( let the moat be the base of this triangle ) = 14 foot
Distance from Roma's window to the boat ( let this be the side of the triangle where the right angle is present ) =20 feet
Then the length of rope needed ( hypotenuse ) =
= Let us name the triangle that is formed as △ ABC . Then ;
In △ ABC :
AB = the width of moat ( leg of triangle ) = 14 foot
BC = The distance from the window to the moat ( base ) = 20 feet
AC = Length of rope needed ( hypotenuse ) =
= AB ² + BC² = AC² ( according to the pythagoras theorem the square on the hypotenuse will be equal to the sum of the squares on the other two legs )
= 14² + 20² = AC²
= 196 + 400 = AC²
= 596 = AC²
= 24 × 24 = AC × AC
= 24 foot = AC = length of rope needed by jules .
Therefore , Jules will need a 24 foot rope so that his girlfriend can slide down and escape from her apartment .