I have an approach . . . but is it acceptable?
Firstly the shape is a sqaure.
Lines have been drawn to 3 corners of the square from a point inside the square.
The smallest line is 3 units, the mid one is 4 units, and the largest is 5 units.
Place the square on a coordinate system.
Let the side of the square be .
Using the Distance Formula, we have:
A * - - - - - - - * B
| * P |
| (x,y) |
- C * - - - - - - - * D -
Subtract (1) from (3): .
. . which simplifies to: . . (4)
Subtract (1) from (2): .
. . which simplifies to: . .(5)
Substitute (4) and (5) into (3): .
. . which simplifies to: . . . . a quadratic in .
Quadratic Formula: .
. . The second root is too small be the side of the square.
Therefore, the side of the square is about units.
Edit: corrected errors in last four lines.