Question

question the sides of a triangle are 24, 26, and 10. use the pythagorean theorem to determine if the triangle is right, acute, or obtuse. answer the triangle is because the square of the largest side the sum of the squares of the other two sides.

Explanation:

Step1: Identify the largest side and the other two sides

The largest side $c = 26$, and the other two sides $a = 24$, $b = 10$.

Step2: Calculate the square of the largest side and the sum of the squares of the other two sides

The square of the largest side $c^{2}=26^{2}=676$. The sum of the squares of the other two sides $a^{2}+b^{2}=24^{2}+10^{2}=576 + 100=676$.

Step3: Compare the two values

Since $c^{2}=a^{2}+b^{2}$, by the Pythagorean - Theorem converse, the triangle is a right - triangle.

Answer:

The triangle is right because the square of the largest side equals the sum of the squares of the other two sides.