Question

the sides of a triangle are 61, 39, and 97. use the pythagorean theorem to determine if the triangle is right, acute, or obtuse.

answer attempt 1 out of 2

the triangle is ▼ because the square of the largest side ▼ the sum of the squares of the other two sides.

Explanation:

Step1: Identify largest side, label sides

Largest side: $c=97$, other sides: $a=61$, $b=39$

Step2: Calculate $c^2$

$c^2 = 97^2 = 9409$

Step3: Calculate $a^2 + b^2$

$a^2 + b^2 = 61^2 + 39^2 = 3721 + 1521 = 5242$

Step4: Compare the two values

$9409 > 5242$, so $c^2 > a^2 + b^2$

Answer:

The triangle is obtuse because the square of the largest side is greater than the sum of the squares of the other two sides.