SOLUTION: Theo is building a garden against his house. He bought two pieces of wood that are each five feet long. He wants to create a triangular garden against his house using the two piece

Question 1114077: Theo is building a garden against his house. He bought two pieces of wood that are each five feet long. He wants to create a triangular garden against his house using the two pieces of wood, without cutting them. His house will be the third side of the triangle. He also wants the perimeter of his garden to be a whole number.
There are
different triangles he can create that fit these conditions.
Of these triangles, there are
isosceles,
scalene, and
equilateral.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

If two sides of the garden are the two uncut 5-foot pieces of wood, then at least two sides of the triangular garden will be the same length; there will be no solutions that are scalene triangles, as the wording of the problem says.

The length of the third side of the garden (against the house) must be less than the sum of the lengths of the other two sides; since he wants the perimeter to be a whole number, the length of the third side can be any integer from 1 to 9 inclusive.

So there are 9 different triangles he can make; 8 of them are isosceles and one is equilateral.
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