Question

A
ladder
is placed against
wall such
that its foot is at a distance of 8 m from the wall
And its top reaches a window 6 m above the ground
Find the length of the ladder

Answer 1

Answer:-

The Length Of The Ladder Is 10 m.

Explanation:-

Given:-

• Distance between the foot of the ladder and the wall (AB) = 8 m.

• Height of the window (AC) = 6 m.

ToFind:-

• The length of ladder.

Theorem Used:-

• Pythagoras Theorem:- In a right angle triangle Square of Hypotenuse is equal to the sum of the square of its base and height.

$\\ \large\bf\longrightarrow H^2 = P^2 + B^2.$

Where,

• H = Hypotenuse.
• P = Perpendicular I.e. height.
• B = Base.

So Here,

• H = Length Of ladder = ?? [To Find].

• P = AC = 6 m.

• B = AB = 8 m.

Now,

By Applying Pythagoras Theorem,

$\\ \bf\mapsto H^2 = P^2 + B^2.$

$\\ \tt\mapsto H {}^{2} = (6 \: m) {}^{2} + (8 \: m) {}^{2} .$

$\\ \tt\mapsto H = \sqrt{36 \: m {}^{2} + 64 \: m {}^{2} } .$

$\\ \tt\mapsto H = \sqrt{100 \: m {}^{2} }$

$\\ \tt\mapsto H = \sqrt{10 \times 10} \: \: m .$

$\\ \large\bf\mapsto H = 10 \: m.$

Therefore The Length Of The Ladder Is H = 10m.

Answer 2

AnsWer :

$\setlength{\unitlength}{1.5cm}\begin{picture}(6,2)\linethickness{0.5mm}\put(7.7,2.9){\large\sf{P}}\put(7.7,1){\large\sf{Q}}\put(10.6,1){\large\sf{R}}\put(8,1){\line(1,0){2.5}}\put(8,1){\line(0,2){1.9}}\qbezier(10.5,1)(10,1.4)(8,2.9)\put(7.1,2){\sf{\large{8 m}}}\put(9,0.7){\sf{\large{6 m}}}\put(8.2,1){\line(0,1){0.2}}\put(8,1.2){\line(3,0){0.2}}\end{picture}$

• PR is the ladder.

• QR is the distance between base and ladder.

• PQ is height of the window.

$\bigstar \: \underline{\sf Now,by \: using \: Phythagoras \: theorem \: we \: get : }$

$:\implies \sf (Hypotenuse)^{2} = (Perpendicular)^{2} + (Base)^{2}$

$:\implies \sf (PR)^2 = (PQ)^2 + (QR)^2$

$:\implies \sf PR^2 = (6 \: m)^{2} + (8 \: m)^{2}$

$:\implies \sf PR^2 = 36 + 64$

$:\implies \sf PR= \sqrt{36 + 64}$

$:\implies \sf PR= \sqrt{100}\:m^2$

$:\implies \underline{ \boxed{ \sf PR= 10 \: meter}}$

$\therefore\:\underline{\textsf{Length of the ladder is \textbf{10 meter}}}.$