Question

3. A 15 m long ladder reached a window 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.
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Answer 1

✬ Distance = 9 m ✬

Step-by-step explanation:

Given:

• Length of ladder is 15 m.
• Height of window is 12 m.

To Find:

• Distance between the foot of ladder and wall ?

Solution: Let AB be a window and AC be a ladder and BC be the distance between the foot of ladder and wall.

Here in right angled ∆ABC we have

• AB {perpendicular} = 12 m
• AC {hypotenuse} = 15 m
• ∠ABC = 90° {window will be perpendicular to wall}
• BC = To be calculated

Applying Pythagoras theorem in ∆ABC

★ H² = Perpendicular² + Base² ★

$\implies{\rm }$ AC² = AB² + BC²

$\implies{\rm }$ 15² = 12² + BC²

$\implies{\rm }$ 225 = 144 + BC²

$\implies{\rm }$ 225 – 144 = BC²

$\implies{\rm }$ √81 = BC

$\implies{\rm }$ 9 = BC

Hence, the distance of the foot of the ladder from wall is 9 m.

Answer 2

Answer:

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

Step-by-step explanation:

Let AC be the ladder and A be the window.

Given: AC=15m, AB=12m, CB=am

In right angled triangle ACB,

(Hypotenuse)2  =(Base)2  +[Perpendicular)2  [By Pythagoras theorem]

⇒(AC)²  =(CB)²  +(AB)²

 ⇒(15)² =(a)²  +(12)²

⇒225=a²  +144

⇒a²  =225−144=81

⇒a= √81 =9cm

Thus, the distance of the foot of the ladder from the wall is 9m.