Question

the sides of a triangle are 27, 17, and 13. use the pythagorean theorem to determine if the triangle is right, acute, or obtuse.
the triangle is obtuse - because the square of the largest side dropdown the sum of the squares of the other two sides.
dropdown options: is greater than, equals, is less than

Explanation:

Step1: Identify the largest side

The sides are 27, 17, 13. The largest side is 27.

Step2: Calculate squares of sides

Calculate \(27^2 = 729\), \(17^2 = 289\), \(13^2 = 169\).

Step3: Sum of squares of smaller sides

Sum of squares of 17 and 13: \(289 + 169 = 458\).

Step4: Compare with square of largest side

Compare 729 (square of 27) with 458 (sum of squares of 17 and 13). Since \(729>458\), by the Pythagorean inequality theorem, if \(c^2 > a^2 + b^2\) (where \(c\) is the largest side), the triangle is obtuse. So the square of the largest side is greater than the sum of the squares of the other two sides.

Answer:

is greater than