A ladder is resting against a vertical wall and its bottom is 2.5 m away from the wall. If it slips 0.8 m down the wall, then its bottom will move away from the wall by 1.4 m. What is the length of the ladder?

Calcualation:

Here, AD and BE are the same ladders.

So, AD = BE

In Δ ACD,

AD² = AC² + CD² = (y + 0.8)² + 2.5²

In Δ BCE,

BE² = BC²+ CE² = y² + (2.5 + 1.4)² = y² + 3.9²

Since, AD = BE

So, AD² = BE²

(y + 0.8)2 + 2.52 =  y2 + 3.92

⇒ y² + (0.8)² + 2 × y × 0.8  + 6.25 = y² + 15.21

⇒ 0.64 + 1.6y + 6.25 = 15.21

⇒ 1.6y = 15.21 - 0.64 - 6.25 = 8.32

⇒ y = 8.32 / 1.6 = 5.2

So,

AD² =  (y + 0.8)2 + 2.52 = (5.2 + 0.8)² + 2.5² = 36 + 6.25 = 42.25

So, Length of the ladder = AD = √42.25 = 6.5 m

∴ The correct answer is option (2).