Question

a triangle has sides with lengths of 49 miles, 55 miles, and 21 miles. is it a right triangle

Explanation:

Step1: Check the Pythagorean theorem

The Pythagorean theorem states that for a right - triangle with sides \(a\), \(b\), and hypotenuse \(c\) (where \(c\) is the longest side), \(a^{2}+b^{2}=c^{2}\).
Let \(a = 21\), \(b=49\), and \(c = 55\) (since \(55>49>21\)).
Calculate \(a^{2}+b^{2}\):
\(a^{2}+b^{2}=21^{2}+49^{2}=441 + 2401=2842\)
Calculate \(c^{2}\):
\(c^{2}=55^{2}=3025\)

Step2: Compare the two results

Since \(2842
eq3025\) (i.e., \(a^{2}+b^{2}
eq c^{2}\))

Answer:

no