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students are sitting in an auditorium in such a manner that there are as many student there are rows in the auditorium. How many rows are there in the auditorium
Answers
Step-by-step explanation:
Let there be
′
a
′
rows in the auditorium
Since the number of students in a row is same as the number of rows in the auditorium.
∴ Number of students in a row =a
⇒ Number of students in
′
a
′
rows =a×a=a
2
It is given that the total number of students in the auditorium =5929.
∴a
2
=5929
⇒a=
5929
7∣5929
7∣847
11∣121
∣11
⇒a=
(7×7)×(11×11)
[By prime factorisation]
⇒a=7×11 [Taking one factor in each pair]
⇒a=77
Hence, there are 77 rows in the auditorium.
Answer:
Let there be
′
a
′
rows in the auditorium
Since the number of students in a row is same as the number of rows in the auditorium.
∴ Number of students in a row =a
⇒ Number of students in
′
a
′
rows =a×a=a
2
It is given that the total number of students in the auditorium =5929.
∴a
2
=5929
⇒a=
5929
7∣5929
7∣847
11∣121
∣11
⇒a=
(7×7)×(11×11)
[By prime factorisation]
⇒a=7×11 [Taking one factor in each pair]
⇒a=77
Hence, there are 77 rows in the auditorium.
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Step-by-step explanation:
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