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The lengths of two sides of an isosceles triangle are $15$ and $22$, respectively, what are the possible values of perimeter?

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Hint: Here we need to apply the concept of isosceles triangle and perimeter of triangle.
Isosceles Triangle: The triangle in which the two sides of a triangle are equal, then the angles opposite to equal sides are also equal.
Perimeter of triangle = Sum of all sides.

Complete step by step answer:
As the property of a triangle states that in an isosceles triangle two sides of a triangle are equal.
As two sides of a triangle are given as \[15\] and \[22\], respectively.
We can fix either the two equal sides as \[15\] and the third side is \[22\] (or) the two equal sides as \[22\] and the third side is \[15\].
The sides of triangle can be either $15,15,22$ or $15,22,22$

Perimeter of the triangle = Sum of three sides of a triangle
Perimeter of the triangle = $15+22+22=59$ or $15+15+22=52$
Therefore, the possible values of the perimeter are $59\text{ or 52}$ .

Note: In such types of questions the concept of triangles knowing about the properties and types of triangles and the formula related to the triangle is needed. Here the given information is assigned in the formula and the required value is calculated.