Question

The lengths of the sides of a triangle are 3, 3, 3 square root 2 Can the triangle be a right triangle?

Answer 1

The triangle can be a right triangle according to the Pythagorean theorem.

Step-by-step explanation:

To determine if a triangle is a right triangle, we can use the Pythagorean theorem. According to the Pythagorean theorem, in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (hypotenuse).

In this case, the lengths of the sides are 3, 3, and 3√2. Let's calculate: (3)² + (3)² = 18 and (3√2)² = 18. Since the two values are equal, the triangle satisfies the Pythagorean theorem and can be a right triangle.

Answer 2

Step-by-step explanation:

If the base and height were each 3, then the hypotenuse would need to be:

3^2 + 3^2 = C^2

9 + 9 = C^2

18 = C^2

C = SQRT(18) = 4.24

This is larger than sqrt(3), so this cannot be a right triangle.