40-40 isosceles triangle
How many different triangles are there, which satisfy the following properties:
- The triangle is isosceles.
- The triangle has an angle which is .
- The triangle has a side of length 40.
Details and assumptions
2 triangles are different if they are not congruent.
Rotations, reflections and translations of a triangle are considered the same.
The answer is 4.
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1 solution
From the first and second conditions, the triangle must either be 4 0 ∘ − 4 0 ∘ − 1 0 0 ∘ or 4 0 ∘ − 7 0 ∘ − 7 0 ∘ .
To satisfy the third condition, either the equal sides, or the base of the triangle must be equal to 40. This gives 2 × 2 = 4 different triangles which satisfy the conditions.