Question

A 15m long ladder reaches a window 12m high from the ground on placing it against a wall. how far is the foot of the ladder from the wall?​

Answer 1

A 15m long ladder reaches a window 12m high from the ground on placing it against a wall. How far is the foot of the ladder from the wall?

Answer : 9 metres

Refer the attachment for figure.

Step by step explanation :

In given figure,

AC = 15 metres long ladder

AB = 12 metres high

CB = 'a' metres

Now,

∆ ABC is a right angled triangle.

Angle ABC = 90°.

By Pythagoras theorem,

(AC)^2 = (BC)^2 + (AB)^2

(15)^2 = (a)^2 + (12)^2

225 = (a)^2 + 144

225 - 144 = (a)^2

81 = (a)^2

9 = a

Therefore, the foot of the ladder is 9 metres away from the wall.

__________________________

Answer 2

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A 15 m long ladder reaches a window 12 m high from the ground on placing it against a wall. How far is the foot of the ladder from the wall ?​

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Refer to the pic attached for the figure of this question.

By the Pythagoras Theorem in Triangle ABC :-

$\tt{AB^{2} + CB^{2} = AC^{2}}$

Put the values in the formula and then solve it.

$\tt{12^{2} + x^{2} = 15^{2}}$

Solve it further

$\tt{x^{2} = 225 - 144}$

Some more steps to go

$\tt{x^{2} = 81}$

x = 9 m

Answer = 9 m