Ruling on one who prays on a carpet, the edges of which reach the bathroom

Firstly: 

In
order for prayer to be valid, it is stipulated that the person’s clothes and
body, and the place where he prays, should be pure and clean. If a person
knowingly prays on unclean ground, or in an unclean garment, or with an
unclean substance on his body, then his prayer is not valid. Allah, may He
be exalted, says (interpretation of the meaning): “And
your garments purify!”
[al-Muddaththir 74:4]

It was
narrated from Asma bint Abi Bakr as-Siddeeq that she said: A woman asked the
Messenger of Allah (blessings and peace of Allah be upon him): O Messenger
of Allah, what do you think if menstrual blood gets on the garment of one of
us, what should she do? The Messenger of Allah (blessings and peace of Allah
be upon him) said: “If menstrual blood gets on the garment of one of you,
let her scratch it off and sprinkle it with water, then let her pray in it.”

Narrated by al-Bukhaari (307) and Muslim (291). 

Ibn
‘Abd al-Barr (may Allah have mercy on him) said: This hadeeth is the main
guideline on washing the impurities from clothes.

End
quote from al-Istidhkaar, 1/291 

An-Nawawi (may Allah have mercy on him) said: Our view is that removing
impurities is a condition of prayer being valid, whether it is an obligatory
or supererogatory (naafil) prayer, or a funeral prayer, or the prostration
of recitation, or the prostration of thankfulness. Removal of impurities is
stipulated in all cases. This is our view and it is also the view of Abu
Haneefah, Ahmad and all the scholars of the earlier and later generations. 

Three
reports were narrated from Maalik about removing impurities, the soundest
and most well known of which is that if a person prays knowing that some
impurity is present, his prayer is not valid, but if he was not aware of it
or he forgot, then it is valid. This is an older view narrated from
ash-Shaafa‘i, and his later view is that the prayer is not valid, whether he
was aware of it or not, or he forgot.

End
quote from al-Majmoo‘, 3/139 

Shaykh
‘Abdullah ibn Saalih al-Fawzaan (may Allah preserve him) said: This
indicates that one should not pray in an unclean garment; rather one should
pray in a clean and pure garment. This is among the strongest evidence that
it is obligatory to purify one’s garments for prayer.

End
quote from Minhah al-‘Allaam Sharh Buloogh al-Maraam (1/1808) 

Secondly: 

If a
person prays on a carpet, the edge of which is impure or in contact with
something impure, or it is spread over something that is impure, his prayer
is still valid, because he is not in direct contact with the impurity. 

Ibn
Qudaamah (may Allah have mercy on him) said: If he prays on a cloth, the
edge of which is impure, or if there is beneath his feet of rope that is
tied to something impure, but what he is praying on is pure, then his prayer
is valid, regardless of whether or not the impurity moves when he moves.
That is because he is not carrying the impurity and is not praying on it;
rather his prayer mat is in contact with it. This is like if he prays on
pure ground that is connected to impure ground.

End
quote from al-Mughni (402). 

An-Nawawi (may Allah have mercy on him) said: If there is any impurity on
the carpet or mat and the like, and he prays on the spot where the impurity
is, then his prayer is not valid, but if he prays on a clean spot of the
mat, then his prayer is valid. Our companions said: (This applies)
regardless of whether or not the carpet moves when he moves, because he is
not carrying or touching the impurity. The same applies if he prays on a bed
the feet of which are standing on something impure; his prayer is valid,
even if it moves when he moves.

End
quote from al-Majmoo‘ (3/159). 

Based
on the above, if a person prays in a room in which there is something
impure, or he prays on the carpet, the edge of which is impure, or that is
spread over something impure, but he does not have any direct contact with
the impurity, then his prayer is valid. 

Note: 

Places
where people pray or other places cannot be ruled to be impure unless it is
known that impurity has indeed gotten onto them. The fact that people walk
on the carpet after they come out of the washroom does not necessarily imply
that the carpet has become impure. The basic principle is that this place is
definitely pure and that there is some doubt concerning impurity. One of the
ways in which Islam makes things easy for people is that the basic principle
that a thing is definitely pure remains in effect and we do not rule that a
place is impure unless it is known that it has indeed become impure. 

And
Allah knows best.