the lengths of two sides of a triangle are 15 inches each and the third side measures 10 inches what kind of triangle is that

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If two sides have the same length, the triangle is isosceles.

To determine the type of triangle you have with the given side lengths (15 inches, 15 inches, and 10 inches), we can use the Triangle Inequality Theorem.

According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's check if this condition is satisfied for the given side lengths:
- For the sides measuring 15 inches and 15 inches: 15 + 15 = 30 inches
- For the remaining side measuring 10 inches

Since 30 is greater than 10, the condition is satisfied. Therefore, a triangle can be formed with these side lengths.

Now, let's consider the type of triangle:
1. If all three sides of a triangle are equal in length, it is an equilateral triangle.
2. If two sides of a triangle are equal in length, it is an isosceles triangle.
3. If all three sides of a triangle have different lengths, it is a scalene triangle.

In this case, since two sides are equal in length (15 inches), it is an isosceles triangle.