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## Homework Statement

This question is taken from 2011 Malaysian Mathematical Olympiad.

Mary is standing in a rectangular garden. Her distance to the four corners of the garden are 6 m, 7 m, 9 m and d m, respectively, where d is an integer. Find d.

## Homework Equations

Triangle inequality. a + b < c, a + c < b, b + c < a, where a, b, and c are the lengths of the three sides of the triangle.

## The Attempt at a Solution

I tried to denote the length of the rectangular garden as a and b, respectively, then from the four triangles formed, I formed some inequality and try to see if the value of d is bounded, but it yields nothing. I have also tried to solve for d by using the concept of area. Also, I tried using the law of cosine and the Pythagorean theorem. But still, I can't find the value for d.

Any other ideas how to approach this problem? Thanks. :)