Question

a 10m long ladder reached a window 6m from the ground on placing its against wall at a distance x. find the distance x (draw the diagram​

Answer 1

A N S W E R :

• Distance (x) of ladder from wall = 8 m

$\underline{\frak{\qquad Given : \qquad}}$

• Length of ladder = 10 m
• Distance of window from ground = 6 m

$\underline{\frak{\qquad To\:Find : \qquad}}$

• Distance (x) of ladder from wall = ?

$\underline{\frak{\qquad Solution : \qquad}}$

By using Phythagoras theorem :

• Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle :]

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

$\tt {\pink{Here}}\begin{cases} \sf{\green{Hypotenuse= 10\: m}}\\ \sf{\blue{Perpendicular= 6\: m}}\\ \sf{\orange{Base= x}}\end{cases}$

$:\implies \sf (10)^2 = (6)^2 + (x)^2$

$:\implies \sf 100 = 36+ x^2$

$:\implies \sf x^2 = 100 - 36$

$:\implies \sf x^2 = 64$

$:\implies \sf x = \sqrt{64 }$

$:\implies \underline{ \boxed{ \sf x = 8 \: m }}$

$\therefore\:\underline{\textsf{The distance (x) of ladder from wall is \textbf{8 m}}}.$

Answer 2

$\huge{\boxed{\rm{\red{Question}}}}$

A 10m long ladder reached a window 6m from the ground on placing its against wall at a distance x. Find the distance x.

$\huge{\boxed{\rm{\red{Answer}}}}$

${\bigstar}\large{\boxed{\sf{\pink{Answer}}}}$

$\bold{\blue{\fbox{\green{Distance of ladder from the wall = 8 metres}}}}$

$\bold{\blue{\fbox{\green{Diagram is in above attachment}}}}$

${\bigstar}\large{\boxed{\sf{\pink{Given \: that}}}}$

• Length of the ladder = 10 metres.
• Distance of window from ground = 6 metres.

${\bigstar}\large{\boxed{\sf{\pink{To \: find}}}}$

• Distance of lader from the wall {x}

${\bigstar}\large{\boxed{\sf{\pink{Solution}}}}$

$\large\red{\texttt{By using Phythagoras Theorm}}$

$\large\red{\texttt{Formula of Phythagoras Theorm →}}$

Hyputenuse² = Perpendicular² + Base²

$\large\blue{\texttt{Here we have}}$

$\large\orange{\texttt{Hypotenuse = 10 m}}$

$\large\orange{\texttt{Perpendicular = 6 m}}$

$\large\orange{\texttt{Base = x metres}}$

☞ 10² = 6² + x²

☞ 100 = 36 + x²

☞ x² = 100 - 36

☞ x² = 64

☞ √64

$\large\purple{\texttt{√ means square root}}$

☞ 8 metres

$\bold{\blue{\fbox{\green{Distance of ladder from the wall = 8 metres}}}}$

$\huge\mathtt\purple{\boxed{\underline\red{\overbrace\green{Aid \: to \: memory}}}}$

$\large\mathtt\orange{\boxed{\underbrace\pink{\overbrace\blue{Phythagoras \: theorm}}}}$

Pythagoras theorem states that “ In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”. The sides of the right-angled triangle are called base, perpendicular and hypotenuse .

$\large\mathtt\orange{\boxed{\underbrace\pink{\overbrace\blue{Square \: Root}}}}$

A number which produces a specified quantity when multiplied by itself is known to be square root.

@Itzbeautyqueen23

Hope it's helpful

Thank you.