Question

1. A ladder 20 m long reaches the
window of a house 16 m above the
ground. Find the distance of the foot
of the ladder from the base of the
wall. *​

Answer 1

Given :-

A ladder of 20 meters long reaches the window of a house of 16 meters above the ground .

Required to find :-

• The distance of the foot of the ladder from the base of the wall ?

Theorem used :-

$\tt \bf \red{ Pythagorean \: Theorem}$

Solution :-

Before solving this question first let's draw the situation mentioned in that question ;

Diagram :-

$\setlength{\unitlength}{20} \begin{picture}(5,5) \put(1,1){\line(1,0){4}} \put(5,1){\line(0,1){4}} \put(5,5){\line( - 1, - 1){4}} \put(5.5,2.5){ \tt wall } \put(1.8,3.5){ \tt ladder } \put(1.8,2.8){ \tt 20 \: m } \put(5.25,2){ \tt 16 \: cm }\put(0.5,0.7){ \bf A }\put(5,0.75){ \bf B } \put(5,5.25){ \bf C } \end{picture}$

Here we got an right angled triangle which states the fact that we can use Pythagorean theorem to solve this solution .

Similarly ;

AC = Length of the ladder

BC = Length of the wall

AB = Distance of the foot of the ladder from the ground .

So,

Here by applying Pythagorean theorem ;

we get ,

AC² = AB² + BC²

Since,

AC = 20 meters

BC = 16 meters

This implies ;

( 20 )² = AB² + ( 16 )²

400 = AB² + 256

400 - 256 = AB²

AB² = 400 - 256

AB² = 144

AB = √144

AB = ± 12

AB = + 12 or - 12

Since, the length can't be in negative .

So,

Length of AB = 12 meters

Therefore,

Distance between the wall and foot of the ladder = 12 meters .

Answer 2

Given ,

A ladder 20 m long reaches the

window of a house 16 m above the

ground

We know that , the Pythagoras theorem states that :

In right angled triangle , the square of hypotenuse is equal to the sum of squares of other two sides

$\boxed{ { \sf{(hypotenuse)}^{2} = {(base)}^{2} + {(perpendicular)}^{2} }}$

Thus ,

(20)² = (base)² + (16)²

400 = (base)² + 256

(base)² = 144

base = √144

base = ± 12 m

Since , the length can't be negative

Therefore , the distance of the footof the ladder from the base of thewall is 12 m