Question

A $25m$ ladder is placed against a vertical wall of a building. The foot of the ladder is $7m$ from the base of the building. If the top of the ladder slips $4m$, then the foot of the ladder will slide by:

• A. $5m$
• B. $8m$
• C. $9m$
• D. $15m$

Answer 1

The correct option is B $8m$

The ladder forms a right angled triangle with the wall and the base with length of the ladder being the length of hypotenuse of this triangle.

Hypotenuse $=25$ m

Base $=7$ m

Height $={25}^2-7^2=24$ m

Now the ladder slides. In the new position, the hypotenuse of the new right angled triangle will be the same.

The top slides down by a distance $4m$. Hence, the height is $24-4=20$ m. Let the base slide by a distance $x$. Therefore, hypotenuse $=25$ m

Base $=(7+x)$ m

Height $=20$ m

By Pythagoras Theorem, we get

${25}^2-{20}^2=(7+x{)}^2$

$\therefore (7+x)=15$

Hence, $x=8$

The correct answer is Option B.