Question

Which classification best describes the triangle with side lengths of 21, 33, and 35?

a) Acute
b) Obtuse
c) Right
d) None of the above

Answer 1

The triangle with side lengths of 21, 33, and 35 is an acute triangle, as the square of the longest side is less than the sum of the squares of the other two sides.

Step-by-step explanation:

To determine the classification of the triangle with side lengths of 21, 33, and 35, we use the Pythagorean theorem. A triangle is right-angled if the square of the longest side equals the sum of the squares of the other two sides. In this case:

• 352 = 1225
• 212 + 332 = 441 + 1089 = 1530

Since 1225 is not equal to 1530, the triangle is not right-angled. When the square of the longest side is less than the sum of the squares of the other two sides (1225 < 1530), the triangle is acute. If it were more, it would be obtuse. However, since 1225 is less, the correct answer is:

(a) Acute