Question

A 15 m long ladder reached a window to 12 m high from the ground on placing it against a wall at a distance a .find the distance of the foot of the ladder from the wall.

Answer 1

Given

• A 15 m long ladder reached a window to 12 m high from the ground on placing it against the wall at a distance 'a'.

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To Find

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

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Solution

When the ladder is placed against a wall, we see that it forms a right-angled triangle.

Hence we will be using the Pythagorean Theorem to find the distance of the foot of the ladder from the wall.

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

Here,

Base → a m

Height → 12 m

Hypotenuse → 15 m

Let's solve the below equation to find the value of the base.

(a)² + (12)² = (15)²

Step 1: Simplify the equation.

⇒ (a)² + (12)² = (15)²

⇒ a² + 144 = 225

Step 2: Subtract 144 from both sides of the equation.

⇒ a² + 144 - 144 = 225 - 144

⇒ a² = 81

Step 3: Find the square root of both sides of the equation.

⇒ √a² = √81

⇒ a = 9

∴ Base = 9 m

∴ The distance of the foot of the ladder from the wall is 9 m.

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Answer 2

Given :-

A  15 m long ladder reached a window to 12 m high from the ground on placing it against a wall at a distance

To Find :-

The distance of the foot of the ladder from the wall.

Solution :-

By using Pythagoras theorem

$\sf H^2 = P^2 + B^2$

$\sf (15)^2 = (12)^2 + B^2$

$\sf 225 = 144 + B^2$

$\sf 225 - 144 =B^2$

$\sf 81=B^2$

$\sf \sqrt{81} = B$

$\sf 9 =B$