A triangle has side lengths of 3cm, 4cm, and, 6cm. Is it a right triangle explain?

We will be using the concept of  Pythagoras theorem and check whether it is a right-angled triangle or not.

Answer: No, a triangle having side lengths 3cm, 4cm, and, 6cm is not a right triangle.

Let's solve this question step by step.

Explanation:

Let's assume that the given triangle is a right-angled triangle

Here, we are given that

Hypotenuse(h) = 6cm (hypotenuse is the longest side)

Base(b) = 3cm

Altitude(a) = 4cm

According to the Pythagoras theorem, for a given right triangle,

Hypotenuse² = Altitude² + Base²

Thus as per the given dimensions,

h² = ​a² + b²

⇒ h² = 3² + 4² = 9 +16 = 25

According to given hypotenuse h,

h² = 6² = 36

Since they do not match, we cannot have a right triangle with these measures.

We can use the right angle triangle calculator to check whether the given sides of a triangle belong to the right-angled triangle or not.

Hence, it is not a right-angled triangle as the given dimensions (3cm, 4cm, and, 6cm) of the triangle do not satisfy the Pythagoras theorem.