Question

One side of a isosceles triangle is 6cm . What are the possible integer length of the other 2 sides ?

Answer 1

The possible integer lengths of the two equal sides of an isosceles triangle with one side being 6 cm are any integers greater than 3 cm.

Step-by-step explanation:

To determine the possible integer lengths of the other two sides of an isosceles triangle when one side is 6 cm, we can apply the properties of isosceles triangles and the triangle inequality theorem. The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

For an isosceles triangle with one side of 6 cm, let's call the equal sides x (because an isosceles triangle has two sides that are equal in length). The possible lengths of these sides must satisfy two conditions:

1. The sum of the lengths of the two equal sides (x + x) must be greater than 6 cm. Therefore, 2x > 6, which implies that x > 3.
2. Also, the difference of the lengths of the two equal sides (x - x = 0) must be less than 6 cm, which is always true in this case as the sides are equal.

Therefore, the possible integer lengths of the other two sides can be any integer greater than 3 cm. Considering practical length measurements for a real triangle, we have a lower limit of 4 cm. The upper limit would be driven by the physical constraints of triangle construction or the specific problem context. However, without additional constraints, there is no theoretical upper limit as long as x remains an integer.