Question

apply the pythagorean theorem to determine whether a triangle with sides 10 cm, 24 cm, and 25 cm is a right triangle. (1 point)
the triangle is a right triangle because 10+24=25+9.
the triangle is not a right triangle because 10 + 24 ≠ 25.
the triangle is a right triangle because 10² + 24² = 676.
the triangle is not a right triangle because 10² + 24² ≠ 25².

Explanation:

Step1: Recall the Pythagorean Theorem

For a right - triangle with sides \(a\), \(b\) (legs) and \(c\) (hypotenuse), \(a^{2}+b^{2}=c^{2}\). Here, \(c\) is the longest side. So \(a = 10\), \(b=24\), \(c = 25\).

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

\(a^{2}+b^{2}=10^{2}+24^{2}=100 + 576=676\).

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

\(c^{2}=25^{2}=625\).

Step4: Compare \(a^{2}+b^{2}\) and \(c^{2}\)

Since \(10^{2}+24^{2}=676\) and \(25^{2}=625\), and \(676
eq625\).

Answer:

The triangle is not a right triangle because \(10^{2}+24^{2}
eq25^{2}\).