Hi Andrew,
Divide up the octagon as in the diagram.
The octagon is then partitioned into
1 square of area s^{2} square inches
4 rectangles, each of area s a square inches
4 triangles, each of area a^{2} square inches
The sum of the areas of these 9 regions is 289 square inches so
s^{2} + 4 s a + 4 a^{2} = 289
Use Pythagoras Theorem with triangle PQR to write a as a function of s, substitute into the equation above and solve for s.
Penny
