An isosceles triangle has at least two congruent sides. The perimeter of a certian isosceles triangle is at most 12 in. The length of each of the two congruent sides is 5 in. What are the possible lengths of the remaning side

Answer 1

Let's assume that the length of the remaining side is $x$ inches. Since the triangle is isosceles, the two congruent sides have length 5 inches each. Therefore, the perimeter of the triangle can be expressed as:

$5 + 5 + x = 10 + x$

We are given that the perimeter is at most 12 inches. Therefore, we can write the inequality:

$10 + x \leq 12$

Subtracting 10 from both sides, we have:

$x \leq 2$

So the possible lengths of the remaining side are any value less than or equal to 2 inches.