The diagonal of a square forms two 45-45-90 triangles.
The ratios of the lengths of the sides of a 45-45-90 triangle are
[tex] 1~:~1~:~\sqrt{2} [/tex]
The hypotenuse is [tex] \sqrt{2} [/tex] times the length of the legs.
Each leg is the length of the hypotenuse divided by [tex] \sqrt{2} [/tex].
[tex] leg = \dfrac{34}{\sqrt{2}} = 24.0416 [/tex]
[tex] perimeter = 4 \times side [/tex]
[tex] perimeter = 4 \times 24.0416 [/tex]
[tex] perimeter = 96.166 [/tex]
Answer: he will need 96.2 ft of fencing.
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