Question

1. joanie is cutting pieces of colored string to create an obtuse triangle for an art project. the two shorter sides of the triangle measure 10 inches and 12 inches. can joanie create an obtuse triangle by using a 16 - inch piece of string for the third side? explain.

Explanation:

Step1: Recall the obtuse triangle condition

For a triangle with sides \(a\), \(b\), \(c\) (\(c\) is the longest side), if \(a^{2}+b^{2}

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

Calculate \(a^{2}+b^{2}\):
\(a^{2}+b^{2}=10^{2}+12^{2}=100 + 144=244\)
Calculate \(c^{2}\):
\(c^{2}=16^{2}=256\)

Step3: Compare \(a^{2}+b^{2}\) and \(c^{2}\)

Since \(244<256\) (i.e., \(a^{2}+b^{2}

Answer:

Yes, Joanie can create an obtuse triangle. Because for a triangle with side - lengths \(a = 10\), \(b = 12\), \(c = 16\) (where \(c\) is the longest side), \(a^{2}+b^{2}=10^{2}+12^{2}=244\) and \(c^{2}=16^{2}=256\), and \(a^{2}+b^{2}