Question

tell whether the triangle with side lengths of 1 inch, 2.4 inches, and 2.6 inches is a right triangle the triangle a right triangle.

Explanation:

Step1: Recall the Pythagorean theorem

For a triangle with side lengths \(a\), \(b\), and \(c\) (\(c\) is the longest side), if \(a^{2}+b^{2}=c^{2}\), then it is a right - triangle. Here \(a = 1\), \(b=2.4\), \(c = 2.6\).

Step2: Calculate \(a^{2}+b^{2}\)

\(a^{2}+b^{2}=1^{2}+(2.4)^{2}=1 + 5.76=6.76\)

Step3: Calculate \(c^{2}\)

\(c^{2}=(2.6)^{2}=6.76\)

Answer:

Since \(a^{2}+b^{2}=c^{2}\) (where \(a = 1\), \(b = 2.4\), \(c=2.6\)), the triangle is a right - triangle.