Question

can a triangle be made with sides of 9, 18, 27?

Explanation:

Step1: Recall Triangle Inequality Theorem

The triangle inequality theorem states that for a triangle with side lengths \(a\), \(b\), and \(c\), the sum of any two sides must be greater than the third side. Mathematically, this means \(a + b>c\), \(a + c>b\), and \(b + c>a\).

Step2: Check the sum of the two smaller sides

The side lengths are 9, 18, and 27. The two smaller sides are 9 and 18. Their sum is \(9 + 18=27\).

Step3: Compare with the third side

According to the triangle inequality theorem, the sum of the two smaller sides must be greater than the third side. But here, \(9 + 18 = 27\), which is not greater than 27 (it's equal). So, the triangle inequality is not satisfied.

Answer:

No, a triangle cannot be made with sides of 9, 18, and 27.