ANSWER
34 ft
EXPLANATION
The wooden border around the sandbox is the perimeter of the sandbox.
Note that, the sides of the kite are the diagonals of an invisible right triangle. See attachment.
We can use the Pythagoras Theorem to find the length of the longer side
[tex] {x}^{2} = {8}^{2} + {6}^{2} [/tex]
[tex] {x}^{2} = 64 +36[/tex]
[tex] {x}^{2} = 100[/tex]
[tex]x = \sqrt{100} [/tex]
[tex]x = 10 \: units[/tex]
The length of one of the shorter sides is
[tex] {y}^{2} = {4}^{2} + {6}^{2} [/tex]
[tex] {y}^{2} = 16 + 36[/tex]
[tex] {y}^{2} = 52[/tex]
[tex]y = \sqrt{52} [/tex]
[tex]y = 2 \sqrt{13} \: units[/tex]
The length of wood he needs is
[tex]2 \sqrt{13} + 2 \sqrt{13} + 10 + 10 = 20 + 4 \sqrt{13} = 34.42[/tex]
He needs approximately 34 ft of wood.
