Question 1114077
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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.<br>
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.<br>
So there are 9 different triangles he can make; 8 of them are isosceles and one is equilateral.