Posted by **rajshekhar** on Monday, February 1, 2010 at 6:06am.

All the students in a school are made to stand in rows so as to form an equilateral triangle. The first row consists of one student, the second row 2 students, third row 3 students and so on. Had there been 90 more students, the total number of students could have been arranged in the shape of a square, so that each side of the square has 5 students less than the number of students in the side of the triangle. Find the total number of students initially present in the school?

- maths -
**Reiny**, Monday, February 1, 2010 at 10:18am
You are dealing with the triangular numbers whose sums of consecutive rows would be

1 3 6 10 15 21 28 ...

these numbers are generated by (n^2+n)/2 for n equal to the set of natural numbers.

So I added 90 to each of these to see if I get a perfect square.

The first such n value was at n=4

the sum of students would have been 10, and adding 90 gave me 100.

But that did not satisfy the second condition you gave, namely that the side of the square had to be 5 less than the side of the triangle.

I kept going for a while, almost gave up, but came to n = 26

the sum of the students in the triangle is (26^2 + 26)/2 = 351

adding 90 got me 441 which is 21^2

and the difference between these is indeed 5

so there were initially 351 students in the school

## Answer This Question

## Related Questions

- maths - Set it up this way: Let the number of students be x let the number of ...
- maths - students are made to stand in equal rows with equal number of students....
- Math - an auditorium has 50 rows of seats. THe first row has 20 seats, the row ...
- Math - The first row of a concert hall has 25 seats and each row after the first...
- math - Three hundred thirty six students of school A and four hundred thirty two...
- MATH - a pile of bricks has 85 bricks in the bottom row, 79 bricks in the second...
- Combinatorics - There are two rows of seats in the classroom and each row has ...
- maths - 1450 students had to stand in rows and benches no.of row and benches ...
- Math - An auditorium has 150 rows of seats. The first row has 15 seats, the ...
- arithmetic - An auditorium has 20 rows of seats.These are 20 seats in the first ...

More Related Questions