Question

The top of a ladder of length 15m reaches a window 9m above the ground. What is the distance between the base of the wall & that of the ladder?

Answer 1

Answer:

12 m is the answer.

check the attachment for ans.

Answer 2

Given:

$\implies$ The top of a ladder of length 15m reaches a window 9m above the ground

To Find:

$\implies$ The distance between the base of the wall & that of the ladder

_____

Let RQ be the wall & RP the ladder from ΔPQR.

P is the foot of the ladder, Q is the base of the wall, R is the window.

We have to find the distance between the base & the foot of the ladder i.e, the length of Q & P

✦ (Refer to the attachment)

From the given information,

$\implies l \sf{(PQ) = 15m}$

$\implies l \sf{(QR) = 9m}$

Now, to find the length of PQ, let the length of PQ be x meter.

By Pythagoras' Theorem,

$\implies \sf{\bigg[ \textit{l} \sf{(PQ)}\bigg]^2 = \bigg[ \textit{l} \sf{(RQ)}\bigg]^2 + \bigg[ \textit{l} \sf{(RP)}\bigg]^2}$

$\implies \sf{15^2 = x^2 + 9^2}$

$\implies \sf{225 = x^2 + 81}$

$\implies \sf{x^2 = 144}$

$\implies \sf{x^2 = 12^2}$

$\implies \underline{\boxed{\sf{\purple{x = 12}}}}$

   

Final Answer:

The distance between the foot of the ladder & the base of the wall is 12m.