Question

A ladder 13 meter long, reaches a window 12 meter above the ground. Find the distance of the foot of the ladder from the base of the wall.

Answer 1

HINT:-
For this question, we will be using the Pythagoras Theorem as the wall and the ladder are making a right angle, i.e. they are making an angle of 90°.

Complete step-by-step answer:
But before starting the solution, one must know about Pythagoras Theorem.
Pythagoras Theorem is a theorem stating that the square of the length of the Hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other sides, i.e. Perpendicular and Base. It is used to find the length of the sides of a right angled triangle.
Therefore, the ladder will be the hypotenuse, the wall will be the perpendicular and the distance between the foot of the ladder and the wall will be the base.

We know that the Pythagoras Theorem is: \[{{\left( Hypotenuse \right)}^{2}}={{\left( Perpendicular \right)}^{2}}+{{\left( Base \right)}^{2}}\]
And as mentioned above, we are taking the ladder to be the hypotenuse and the wall to be the perpendicular. Therefore, we need to find the base, i.e. is the distance between the foot of the ladder and the wall.
As the formula is \[{{\left( Hypotenuse \right)}^{2}}={{\left( Perpendicular \right)}^{2}}+{{\left( Base \right)}^{2}}\] therefore:-
     \[{{\left( Length\text{ }of\text{ }ladder \right)}^{2}}={{\left( Length\text{ }of\text{ }wall \right)}^{2}}+{{(Distance\text{ from }foot\text{ }of\ ladder\text{ }and\text{ }wall)}^{2}}\]
Now, let us take the distance between the foot of the ladder and the wall to be ‘x’.
Thus,
\[\begin{array}{*{35}{l}}
   {{\left( 13 \right)}^{2}}={{\left( 12 \right)}^{2}}+{{\left( x \right)}^{2}} \\
   169=144\text{ }+{{\left( x \right)}^{2}} \\
   169-144={{\left( x \right)}^{2}} \\
   25={{\left( x \right)}^{2}} \\
\end{array}\]
We know that the square root of 25 is 5.
Therefore,
\[{{\left( x \right)}^{2}}={{\left( 5 \right)}^{2}}\]
5 = x
Hence, the distance between the foot of the wall and the ladder is 5 meter.

Note:- One must always remember the Pythagoras Theorem as it can come in handy.
\[{{\left( Hypotenuse \right)}^{2}}={{\left( Perpendicular \right)}^{2}}+{{\left( Base \right)}^{2}}\]
Hypotenuse is the longest side of a right angled triangle. Also, it is the side opposite to the 90° angle.