Question

A ladder 13 m long is placed on the ground in such a way that is touches the top of a vertical wall 12 m high. Find the distance of the foot of the ladder from the bottom of the wall.

Answer 1

According to pythagoras theorem,

${ab}^{2} = {ac}^{2} + {bc}^{2}$

13×13=(12×12)+bc^2

bc^2=169-144

bc^2=25

bc=5m

Answer 2

The distance of the foot of the ladder from the bottom of the wall is 5 m.

A ladder 13m long is placed on the ground in such a way that touches the top of a vertical wall 12 m high.

We have to find the distance of the foot of the ladder from the bottom of the wall.

Let's draw a rough diagram to understand it better.

Let AC is the ladder on the ground C in such a way that it touches the top of a vertical wall AB. [ shown in figure ]

∵ AB is a vertical wall and BC is horizontal ground. it means AB must be perpendicular on the BC.

∴ ∆ABC is right angled triangle.

from Pythagoras theorem,

AB² + BC² = AC²

here,

• AB = height of wall = 12 m
• BC = distance of foot of ladder to the bottom of wall
• AC = length of ladder = 13

⇒12² + BC² = 13²

⇒BC² = 169 - 144 = 25 = 5²

⇒BC = 5

Therefore the distance of the foot of the ladder from the bottom of the wall is 5 m.