5 + 5 + 16 = 26

when two sides of an isosceles triangle are 5and16

the third =16

(as it mastn't be a triangle when we say that the third=5)

so the perimeter of the triangle =16+16+5=37

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The only solutions to this problem are: ${5,5,16}$ and ${5,16,16}$ But by Triangle Inequality Theorem (or whatever it was called), the length of the hypotenuse is less than the sum of the other two lengths. Hence, we omit ${5,5,16}$ . Thus, the only possible solution is ${5,16,16}$ . Perimeter of the triangle therefore is $5+16+16=37$

Sum of two sides in a triangle should always be greater than the third side -

Case I : When the two sides are 5 ,

5+5<16

Since it doesn't satisfy the condition, thus the two equal sides are 16 ,

So, Perimeter= 5+16+16=37.

Since it's an isosceles triangle, two sides must be equal. Having two sides with length 5 is impossible because they cannot accommodate a last side of 16. The maximum they can accommodate is 10, a straight line. Therefore the triangle must be of two sides 16 and one 5, a perimeter of 37