The lengths of the sides of a triangle are 3, 4, 5. Can the triangle be a right triangle?

Solution:

It is given that

The sides of a triangle are 3, 4, and 5. Let us check if the triangle is a right triangle by finding if the sum of the squares of the lengths of the legs of the triangle is equal to the square of the hypotenuse.

Observe the triangle, with the given dimensions. Using the Pythagorean theorem,

We know that

3² + 4² = 9 + 16 = 25

= 5²

Thus the 3 sides 3,4 and 5 are the Pythagorean triples.

Therefore, the triangle is a right triangle.

The lengths of the sides of a triangle are 3, 4, 5. Can the triangle be a right triangle?

Summary:

The lengths of the sides of a triangle are 3, 4, 5. Yes, the triangle can be a right triangle.