# 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,

**Hypotenuse ^{2}**

**= Altitude**

^{2}**+ Base**

^{2}Thus as per the given dimensions,

h^{2} = a^{2} + b^{2}

⇒ h^{2} = 3² + 4² = 9 +16 = 25

According to given hypotenuse h,

h^{2 }= 6^{2} = 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.

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