Saniya writes a positive integer on each edge of a square. She also writes at each vertex the product of the numbers on the two edges that meet at that vertex. The sum of the numbers at the vertices is 15. What is the sum of the numbers on the edges of the square?

Answer: The sum of the numbers in the edges is 7

Step-by-step explanation:

We have 4 positive integers A, B, C and D.

The numbers in the vertices are:

AB, BC, CD and DA

We know that:

AB + BC + CD + DA = 15.

B (A + C) + D (A + C) = 15

(B + D) (A + C) = 15

The only two numbers that when you multiply them are equal to 15, are 3 and 5. (3*5 = 15)

So we need to have

B + D = 5

A + C = 3

or

B + D = 3

A + C = 5

then:

B + D + A + C = 3 + 4 = 7

The sum of the numbers in the edges is 7