Question

is it possible to draw a triangle with sides of 2, 2, and 5?
it is possible because the sum of any two side lengths must be greater than the third side length.

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 side lengths must be greater than the third side length, i.e., \(a + b>c\), \(a + c>b\), and \(b + c>a\).

Step2: Check the sum of the two smaller sides

Given side lengths \(2\), \(2\), and \(5\). The two smaller sides are \(2\) and \(2\). Their sum is \(2 + 2=4\).

Step3: Compare the sum with the third side

Now, we compare this sum (\(4\)) with the third side (\(5\)). Since \(4<5\), the sum of the two smaller sides is not greater than the third side. So, it does not satisfy the triangle inequality theorem.

Answer:

It is not possible to draw a triangle with sides of \(2\), \(2\), and \(5\) because the sum of any two side lengths (in this case, \(2 + 2 = 4\)) must be greater than the third side length (\(5\)), and \(4\) is not greater than \(5\). So the answers are: "not possible", "no", "greater than" (to fill in the respective blanks: the first blank is "not possible", the second blank is "no", and the third blank is "greater than").