Question

★ELLOH,



$\huge {\mathbb ♡{\orange{QUESTION}\green{♡}\pink{}\blue{!}}}♡$


A 6.5 m long ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall. Find the height of the wall where the top of the ladder touches it?



★ REQUIRED QUALITY ANSWER​

Answer 1

Given

• 6.5 m long ladder is placed against a wall
• Its food is at a distance of 2.5 m from the wall.

____________________________

To Find

• The height of the wall where the top of the ladder touches it.

____________________________

Solution

So let's visualize the scenario. If we think about it carefully we can observe that the ladder placed there forms a right-angled triangle.

(If you require the diagram, I have attached it)

So for this kind of question, we must use the Pythagorean Theorem.

Pythagorean Theorem ⇒ (Base)² + (Height)² = (Hypotenuse)²

Here,

Base = 2.5 m

Hypotenuse = 6.5 m

Height ⇒ x m

Let's solve the following equation to find the height

(2.5)² + x² = (6.5)²

Step 1: Simplify the equation.

⇒ (2.5)² + x² = (6.5)²

⇒ 6.25 + x² = 42.25

Step 2: Subtract 6.25 from both sides of the equation.

⇒ 6.25 + x² - 6.25 = 42.25 - 6.25

⇒ x² = 36

Step 3: Find the square root of 36.

⇒ x² = 36

⇒ x = √36

⇒ x = 6

∴ The height of the wall where the top of the ladder touches is 6 m

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Answer 2

✅ See the attachment diagram.

$\\ \Large{\bf{\green{\underline{GiVeN\::}}}}$

• Length of ladder (AB) = 6.5 m

• Length of foot of the wall (BC) = 2.5 m

$\\ \Large{\bf{\pink{\underline{To\:FiNd\::}}}}$

• The height of the wall where the top of the ladder touches it, i.e. the length of AC.

$\\ \Large{\bf{\purple{\underline{CaLcUlAtIoN\::}}}}$

➣ Here ABC is an rightangle triangle.

↝ According to the question hypotenuse & base is given and we calculate the height of the right angle triangle.

$\bf\blue{Thus,}$

$\bf\red{According\:to\:Pythagoras\:theorem,}$

$\pink\bigstar\:\:{\underline{\green{\boxed{\bf{\purple{(Hypotenuse)^2\:=\:(Height)^2\:+\:(Base)^2}}}}}}$

$\bf\orange{Where,}$

• Hypotenuse = AB

• Height = AC

• Base = BC

$:\implies\:\:\bf{(AB)^2\:=\:(AC)^2\:+\:(BC)^2}$

$:\implies\:\:\bf{(AC)^2\:=\:(AB)^2\:-\:(BC)^2}$

$:\implies\:\:\bf{(AC)^2\:=\:(6.5)^2\:-\:(2.5)^2}$

$:\implies\:\:\bf{(AC)^2\:=\:42.25\:-\:6.25}$

$:\implies\:\:\bf{(AC)^2\:=\:36}$

$:\implies\:\:\bf{AC\:=\:\sqrt{36}}$

$:\implies\:\:\bf{AC\:=\:\pm\:6}$

[NOTE ➛ Value of Length is always a positive integer.]

$:\implies\:\:\bf\green{AC\:=\:6\:m}$

$\Large\bf\blue{Therefore,}$

The height of the wall where the top of the ladder touches it is 6 m.