An isosceles triangle has at least two congruent sides. the perimeter of a certain isosceles triangle is at most 12in. The length of each of the two congruent sides is 5 in. What are the possible lengths of the remaining sides?
Since the triangle is isosceles, we know that the lengths of the two congruent sides are both 5 inches. Let's call the length of the remaining side $x$.
The perimeter of a triangle is the sum of the lengths of all its sides. We are told that the perimeter is at most 12 inches, so we can write the following inequality:
$5 + 5 + x \leq 12$
Simplifying the expression, we have:
$10 + x \leq 12$
Subtracting 10 from both sides:
$x \leq 2$
So the possible lengths of the remaining side are any value less than or equal to 2 inches.