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
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.
Since the isosceles triangle has two congruent sides of 5 inches each, the sum of these two sides would be 5 + 5 = 10 inches.
The perimeter of any triangle is the sum of all its sides. Since the perimeter of this triangle is at most 12 inches, it means that the remaining side cannot be longer than 12 - 10 = 2 inches.
Therefore, the possible lengths of the remaining side are any value less than or equal to 2 inches.