Triangles Online Practice

To determine whether a right triangle can be formed using the given sides \(a = 3\), \(b = 5\), and \(c = 6\), we will apply the Converse of the Pythagorean Theorem.

The Converse of the Pythagorean Theorem states that if \(c\) is the longest side (the hypotenuse) of a triangle, and if \(a^2 + b^2 = c^2\), then the triangle is a right triangle.

First, we need to identify the longest side:

• \(a = 3\)
• \(b = 5\)
• \(c = 6\)

Here, \(c = 6\) is indeed the longest side.

Now, we calculate \(a^2\), \(b^2\), and \(c^2\):

• \(a^2 = 3^2 = 9\)
• \(b^2 = 5^2 = 25\)
• \(c^2 = 6^2 = 36\)

Now, we add \(a^2\) and \(b^2\) together:

• \(a^2 + b^2 = 9 + 25 = 34\)

Now we compare \(a^2 + b^2\) with \(c^2\):

• \(34 \neq 36\)

Since \(a^2 + b^2\) does not equal \(c^2\), the condition for a right triangle is not satisfied.

Thus, the correct response is: No, a right triangle cannot be formed because \(3^2 + 5^2 \neq 6^2\).