# I have two pieces of wood, 22' and 13' long. To make a triangular garden bed how long could the third piece of wood be?

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You have two pieces of wood of lengths 22 and 13 feet. How long could a third piece of wood be to create a triangular bed?

The triangle inequality theorem states that any side of a triangle must be shorter than the sum of the other two sides. Thus we have 2 conditions on the third side:

(1) L<22+13 or L<35 This assumes that the third side is the longest.

(2) L>22-13 or L>9 assuming that the 22 foot piece is the longest.

**Thus the third piece of wood of length L must satisfy 9<L<35**

In a triangle the sum of any two sides has to be greater than the third side.

The triangular garden bed is enclosed by three pieces of wood. The length of two of them is 22' and 13'. The length of the third piece of wood has to be less than the sum of 22' and 13'. As the sum of 22 and 13 is 35, the third piece has to be shorter than 35'.

**The length of the third piece of wood has to be less than 35'.**