Question

A ladder 10m long reaches a window 8m above the ground. Find the distance of the foot of the bladder from base of the wall.​

Answer 1

Given :

• A ladder 10m long reaches a window 8m above the ground.

To Find :

• Distance from foot of the ladder to the base of the wall = ?

Solution :

We have ,

• Length of ladder = 10 m
• Height of wall = 8 m

★ 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 :D

• (Hypotenuse)² = (Base)² + (Height)²

Here,

• Hypotenuse = 10 m
• Base = ?
• Height = 8 m

★ Now, plug in the given values in above formula of Phythagoras theorem :

→ (10)² = (Base)² + (8)²

→ 100 = (Base)² + 64

→ 100 - 64 = Base²

→ 36 = Base²

→ Base = √36

→ Base = 6 m

• Hence ,the distance from foot the ladder to the base of the wall is 6 m.

Answer 2

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

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$\large\underline{\green{\bf Given :-}}$

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• A ladder 10m long reaches a window 8m above the ground

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$\large\underline{\red{\bf To \: Find :-}}$

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

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$\large\underline{\orange{\bf Solution :-}}$

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• Let the distance of the foot of the ladder from base of the wall be "x"

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The given case will rise a right angled triangle with its height as the height of wall , its hypotenuse would be the length of ladder and its base will work as the distance of the foot of the ladder from base of the wall.

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$\underline{\bold{\texttt{By Phythagoras theorem :}}}$

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➠ $\footnotesize{ \sf(Hypotenuse)^2 = (Base)^2 + (Height)^2 \: \: ⚊⚊ ⓵}$

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$\underline{\bold{\texttt{Applying pythagoras theorem in this case :}}}$

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• Hypotenuse = 10 m

• Base = x

• Height = 8 m

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⟮ Putting these values in equation ⓵ ⟯

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➜ (Hypotenuse)² = (Base)² + (Height)²

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➜ (10)² = (x)² + (8)²

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➜ 100 = (x)² + 64

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➜ 100 - 64 = x²

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➜ x² = 36

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➜ $\sf x = \sqrt { 36 }$

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• x = 6
• x = -6

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As length can't be negative hence x = 6

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∴ The distance of the foot of the ladder from base of the wall is 6 m

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