2021 JMC 10 Problems/Problem 7
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Problem
For some real the area of a square equals
and the product of the lengths of its diagonals equals
What is the perimeter of this square?
Solution
Let the square have side length The diagonals have length
So, the product of the length of both diagonals is
and the square's area is
which is half of the product of the diagonals. We have
The area is
implying that the side length is
and the perimeter is