The foot of a ladder 25 m long is 7 m from the base of the building. If the top of the ladder slips by 4 m, then by how much distance will the foot of the ladder slide?

Question

Question

This question was previously asked in

SSC CHSL 2021 (Held On : 24 May 2022 Shift 1)

Answer 1

Given:

Length of the ladder = 25 m

Base distance = 7 m

Concept used:

Hypotenuse² = Perpendicular² + Base²

Calculation:

Let AB be the height of the building, BC be the base distance from the foot of the ladder to the building and AC is the length of the ladder

Applying Pythagoras theorem in ΔABC

AC² = AB² + BC²

⇒ 25² = AB² + 7²

⇒ 625 = AB2 + 49

⇒ 625 - 49 = AB2

⇒ 576 = AB2

⇒ AB = 24

So, the height of the building = 24 m

After the ladder slips by 4 m

Length of the top of the ladder to the foot of the building becomes 24 - 4 = 20 cm

Let DB be the new length and BE be the new base distance from the foot of the ladder to the building

Applying Pythagoras theorem in ΔDBE

DE² = DB² + BE²

⇒ 25² = 20² + BE²

⇒ 625 = 400 + BE2

⇒ 625 - 400 = BE2

⇒ 225 = BE2

⇒BE = 15

So, distance slide by the ladder = CE = 15 - 7

⇒ 8 m.

∴ The foot of the ladder slide is 8 m.

Download Solution PDF