Question

Two side lengths of a triangle are 10 and 25. Which of the following is false?

A) The triangle is a scalene triangle.
B) The triangle is a right triangle.
C) The triangle is an obtuse triangle.
D) The triangle is an acute triangle.

Answer 1

The triangle with side lengths of 10 and 25 cannot be a right triangle.

Step-by-step explanation:

The triangle with side lengths of 10 and 25 cannot be a right triangle or obtuse triangle because it would not satisfy the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

Using the formula a² + b² = c², where a and b are the lengths of the legs and c is the length of the hypotenuse, we can check:

10² + 25² = c²

100 + 625 = c²

725 = c²

This means that the square of the length of the hypotenuse is 725, which is not equal to the sum of the squares of the other two sides.

Therefore, the false statement is B) The triangle is a right triangle.