Question

which type of triangle, if any, can be formed with sides measuring 8 inches, 8 inches, and 3 inches? an equilateral triangle no triangle a scalene triangle an isosceles triangle

Explanation:

Step1: Recall triangle inequality theorem

For a triangle with side lengths \(a\), \(b\), \(c\), the sum of any two sides must be greater than the third side. Let \(a = 8\), \(b = 8\), \(c = 3\).
Check \(a + b>c\): \(8 + 8=16>3\)
Check \(a + c>b\): \(8 + 3 = 11>8\)
Check \(b + c>a\): \(8+3 = 11>8\)
So a triangle can be formed.

Step2: Recall triangle type definitions

• Equilateral: All sides equal. Here two sides are 8, one is 3. Not equilateral.
• Scalene: All sides different. Here two sides are equal (8,8). Not scalene.
• Isosceles: At least two sides equal. Here two sides (8,8) are equal. So it is isosceles.

Answer:

an isosceles triangle